Interpret a confidence interval: A survey organization drew a simple random sample of 625 households from a city of 100,000 households. The sample mean number of people in the 625 households was 2.30: and a 95% confidence interval for the mean number of people in the 100,000 households was 2.16 < μ < 2.44. True or false, and explain: We are 95% confident that the mean number of people in the 625 households is between 2.16 and 2.44. We are 95% confident that the mean number of people in the 100,000 households is between 2.16 and 2.44. The probability is 0.95 that the mean number of people in the 100,000 households is between 2.16 and 2.44. 95% of the households in the sample contain between 2.16 and 2.44 people.

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Answer 1

Textbook Question

Chapter 8.1, Problem 64E

Interpret a confidence interval: A survey organization drew a simple random sample of 625 households from a city of 100,000 households. The sample mean number of people in the 625 households was 2.30: and a 95% confidence interval for the mean number of people in the 100,000 households was 2.16 < μ < 2.44.

True or false, and explain:

We are 95% confident that the mean number of people in the 625 households is between 2.16 and 2.44.
We are 95% confident that the mean number of people in the 100,000 households is between 2.16 and 2.44.
The probability is 0.95 that the mean number of people in the 100,000 households is between 2.16 and 2.44.
95% of the households in the sample contain between 2.16 and 2.44 people.

a.

Expert Solution

To determine

To explain: Whether the statement “We are 95% confident that the mean number of people in the 625 households is between 2.16 and 2.44 .” is true or false.

Answer to Problem 64E

The given statement “We are 95% confident that the mean number of people in the 625 households is between 2.16 and 2.44 .” is false.

Explanation of Solution

Given:

Out of 100,000 households in a certain city 625 units are randomly selected and the mean number of family members is calculated. The mean was 2.30 and a 95% confidence is defined as 2.16<μ<2.44 .

The confidence interval is constructed for the population mean (μ) ; the mean number of family members in all 100,000 households. Here, the mean number of members in the sample households is already calculated to 2.30 .

Hence, the sample mean is fixed an no need to construct a confidence interval for this statistics.

Conclusion:

Therefore, we can conclude that by the confidence interval the mean of the sample is not defined.

b.

Expert Solution

To determine

To explain: Whether the statement “We are 95% confident that the mean number of people in the 100,000 households is between 2.16 and 2.44 .” is true or false.

Answer to Problem 64E

The statement “We are 95% confident that the mean number of people in the 100,000 households is between 2.16 and 2.44 .” is true.

Explanation of Solution

Out of 100,000 households in a certain city 625 units are randomly selected and the mean number of family members is calculated. The mean was 2.30 and a 95% confidence is defined as 2.16<μ<2.44 .

By the notation μ the population mean is denoted. Hence, the interval 2.76<μ<2.88 with 95% confidence level is to definevariation of population mean.

The population that is discussed in this case is all 100,000 households in the city. therefore, he population mean should be the mean number of members in the total number of households.

Conclusion:

Hence, the mean number of people in the 100,000 households have 95% confidence interval between the given interval.

Conclusion:

Here, in the statement it is said that the 95% confidence interval is for the sample mean. Therefore, this statement is said to be false.

c.

Expert Solution

To determine

To explain: Whether the statement “The probability is 0.95 that the mean GPA of all students in the college is between 2.16 and 2.44 .” is true or false.

Answer to Problem 64E

The statement “The probability is 0.95 that the mean GPA of all students in the college is between 2.16 and 2.44 .” is true.

Explanation of Solution

Out of 100,000 households in a certain city 625 units are randomly selected and the mean number of family members is calculated. The mean was 2.30 and a 95% confidence is defined as 2.16<μ<2.44 .

The confidence level of an interval denotes the chance/ probability of the relevant parameter to be within the interval.

Here, the interval 2.16<μ<2.44 is constructed for the population mean with 95% confidence level. Hence, there is 95% chance that the population mean is between 2.16 and 2.44 .

Generally, a probability is expressed as a decimal or fraction. Hence, we should convert this percentage into a decimal to check the statement.

95%=35100=0.95

Conclusion:

Therefore we can conclude that the probability for the mean number of people in total number of households is between the confidence interval is 0.95 .

d.

Expert Solution

To determine

To explain: Whether the statement “ 95% of the households in the sample contain between 2.16 and 2.44 people.” is true or false.

Answer to Problem 64E

The statement “ 95% of the households in the sample contain between 2.16 and 2.44 people.” is false.

Explanation of Solution

Out of 100,000 households in a certain city 625 units are randomly selected and the mean number of family members is calculated. The mean was 2.30 and a 95% confidence is defined as 2.16<μ<2.44 .

As mentioned in the above parts, the confidence interval is defined for the population mean. Hence all the estimations can be made only for the mean number of people in the total number of households in the city.

In the statement the number of peoples in each household is considered individually. It says there is a 95% chance for the number of people in a randomly selected household to be between 2.16 and 2.44 .

Conclusion:

Therefore, we can conclude that the given confidence interval does not represent a proportion of the population.

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Answer 2

Textbook Question

Chapter 8.1, Problem 64E

Interpret a confidence interval: A survey organization drew a simple random sample of 625 households from a city of 100,000 households. The sample mean number of people in the 625 households was 2.30: and a 95% confidence interval for the mean number of people in the 100,000 households was 2.16 < μ < 2.44.

True or false, and explain:

We are 95% confident that the mean number of people in the 625 households is between 2.16 and 2.44.
We are 95% confident that the mean number of people in the 100,000 households is between 2.16 and 2.44.
The probability is 0.95 that the mean number of people in the 100,000 households is between 2.16 and 2.44.
95% of the households in the sample contain between 2.16 and 2.44 people.

a.

Expert Solution

To determine

To explain: Whether the statement “We are 95% confident that the mean number of people in the 625 households is between 2.16 and 2.44 .” is true or false.

Answer to Problem 64E

The given statement “We are 95% confident that the mean number of people in the 625 households is between 2.16 and 2.44 .” is false.

Explanation of Solution

Given:

Out of 100,000 households in a certain city 625 units are randomly selected and the mean number of family members is calculated. The mean was 2.30 and a 95% confidence is defined as 2.16<μ<2.44 .

The confidence interval is constructed for the population mean (μ) ; the mean number of family members in all 100,000 households. Here, the mean number of members in the sample households is already calculated to 2.30 .

Hence, the sample mean is fixed an no need to construct a confidence interval for this statistics.

Conclusion:

Therefore, we can conclude that by the confidence interval the mean of the sample is not defined.

b.

Expert Solution

To determine

To explain: Whether the statement “We are 95% confident that the mean number of people in the 100,000 households is between 2.16 and 2.44 .” is true or false.

Answer to Problem 64E

The statement “We are 95% confident that the mean number of people in the 100,000 households is between 2.16 and 2.44 .” is true.

Explanation of Solution

Out of 100,000 households in a certain city 625 units are randomly selected and the mean number of family members is calculated. The mean was 2.30 and a 95% confidence is defined as 2.16<μ<2.44 .

By the notation μ the population mean is denoted. Hence, the interval 2.76<μ<2.88 with 95% confidence level is to definevariation of population mean.

The population that is discussed in this case is all 100,000 households in the city. therefore, he population mean should be the mean number of members in the total number of households.

Conclusion:

Hence, the mean number of people in the 100,000 households have 95% confidence interval between the given interval.

Conclusion:

Here, in the statement it is said that the 95% confidence interval is for the sample mean. Therefore, this statement is said to be false.

c.

Expert Solution

To determine

To explain: Whether the statement “The probability is 0.95 that the mean GPA of all students in the college is between 2.16 and 2.44 .” is true or false.

Answer to Problem 64E

The statement “The probability is 0.95 that the mean GPA of all students in the college is between 2.16 and 2.44 .” is true.

Explanation of Solution

Out of 100,000 households in a certain city 625 units are randomly selected and the mean number of family members is calculated. The mean was 2.30 and a 95% confidence is defined as 2.16<μ<2.44 .

The confidence level of an interval denotes the chance/ probability of the relevant parameter to be within the interval.

Here, the interval 2.16<μ<2.44 is constructed for the population mean with 95% confidence level. Hence, there is 95% chance that the population mean is between 2.16 and 2.44 .

Generally, a probability is expressed as a decimal or fraction. Hence, we should convert this percentage into a decimal to check the statement.

95%=35100=0.95

Conclusion:

Therefore we can conclude that the probability for the mean number of people in total number of households is between the confidence interval is 0.95 .

d.

Expert Solution

To determine

To explain: Whether the statement “ 95% of the households in the sample contain between 2.16 and 2.44 people.” is true or false.

Answer to Problem 64E

The statement “ 95% of the households in the sample contain between 2.16 and 2.44 people.” is false.

Explanation of Solution

Out of 100,000 households in a certain city 625 units are randomly selected and the mean number of family members is calculated. The mean was 2.30 and a 95% confidence is defined as 2.16<μ<2.44 .

As mentioned in the above parts, the confidence interval is defined for the population mean. Hence all the estimations can be made only for the mean number of people in the total number of households in the city.

In the statement the number of peoples in each household is considered individually. It says there is a 95% chance for the number of people in a randomly selected household to be between 2.16 and 2.44 .

Conclusion:

Therefore, we can conclude that the given confidence interval does not represent a proportion of the population.

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Answer 3

Textbook Question

Chapter 8.1, Problem 64E

Interpret a confidence interval: A survey organization drew a simple random sample of 625 households from a city of 100,000 households. The sample mean number of people in the 625 households was 2.30: and a 95% confidence interval for the mean number of people in the 100,000 households was 2.16 < μ < 2.44.

True or false, and explain:

We are 95% confident that the mean number of people in the 625 households is between 2.16 and 2.44.
We are 95% confident that the mean number of people in the 100,000 households is between 2.16 and 2.44.
The probability is 0.95 that the mean number of people in the 100,000 households is between 2.16 and 2.44.
95% of the households in the sample contain between 2.16 and 2.44 people.

a.

Expert Solution

To determine

To explain: Whether the statement “We are 95% confident that the mean number of people in the 625 households is between 2.16 and 2.44 .” is true or false.

Answer to Problem 64E

The given statement “We are 95% confident that the mean number of people in the 625 households is between 2.16 and 2.44 .” is false.

Explanation of Solution

Given:

Out of 100,000 households in a certain city 625 units are randomly selected and the mean number of family members is calculated. The mean was 2.30 and a 95% confidence is defined as 2.16<μ<2.44 .

The confidence interval is constructed for the population mean (μ) ; the mean number of family members in all 100,000 households. Here, the mean number of members in the sample households is already calculated to 2.30 .

Hence, the sample mean is fixed an no need to construct a confidence interval for this statistics.

Conclusion:

Therefore, we can conclude that by the confidence interval the mean of the sample is not defined.

b.

Expert Solution

To determine

To explain: Whether the statement “We are 95% confident that the mean number of people in the 100,000 households is between 2.16 and 2.44 .” is true or false.

Answer to Problem 64E

The statement “We are 95% confident that the mean number of people in the 100,000 households is between 2.16 and 2.44 .” is true.

Explanation of Solution

Out of 100,000 households in a certain city 625 units are randomly selected and the mean number of family members is calculated. The mean was 2.30 and a 95% confidence is defined as 2.16<μ<2.44 .

By the notation μ the population mean is denoted. Hence, the interval 2.76<μ<2.88 with 95% confidence level is to definevariation of population mean.

The population that is discussed in this case is all 100,000 households in the city. therefore, he population mean should be the mean number of members in the total number of households.

Conclusion:

Hence, the mean number of people in the 100,000 households have 95% confidence interval between the given interval.

Conclusion:

Here, in the statement it is said that the 95% confidence interval is for the sample mean. Therefore, this statement is said to be false.

c.

Expert Solution

To determine

To explain: Whether the statement “The probability is 0.95 that the mean GPA of all students in the college is between 2.16 and 2.44 .” is true or false.

Answer to Problem 64E

The statement “The probability is 0.95 that the mean GPA of all students in the college is between 2.16 and 2.44 .” is true.

Explanation of Solution

Out of 100,000 households in a certain city 625 units are randomly selected and the mean number of family members is calculated. The mean was 2.30 and a 95% confidence is defined as 2.16<μ<2.44 .

The confidence level of an interval denotes the chance/ probability of the relevant parameter to be within the interval.

Here, the interval 2.16<μ<2.44 is constructed for the population mean with 95% confidence level. Hence, there is 95% chance that the population mean is between 2.16 and 2.44 .

Generally, a probability is expressed as a decimal or fraction. Hence, we should convert this percentage into a decimal to check the statement.

95%=35100=0.95

Conclusion:

Therefore we can conclude that the probability for the mean number of people in total number of households is between the confidence interval is 0.95 .

d.

Expert Solution

To determine

To explain: Whether the statement “ 95% of the households in the sample contain between 2.16 and 2.44 people.” is true or false.

Answer to Problem 64E

The statement “ 95% of the households in the sample contain between 2.16 and 2.44 people.” is false.

Explanation of Solution

Out of 100,000 households in a certain city 625 units are randomly selected and the mean number of family members is calculated. The mean was 2.30 and a 95% confidence is defined as 2.16<μ<2.44 .

As mentioned in the above parts, the confidence interval is defined for the population mean. Hence all the estimations can be made only for the mean number of people in the total number of households in the city.

In the statement the number of peoples in each household is considered individually. It says there is a 95% chance for the number of people in a randomly selected household to be between 2.16 and 2.44 .

Conclusion:

Therefore, we can conclude that the given confidence interval does not represent a proportion of the population.

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Answer 4

Textbook Question

Chapter 8.1, Problem 64E

Interpret a confidence interval: A survey organization drew a simple random sample of 625 households from a city of 100,000 households. The sample mean number of people in the 625 households was 2.30: and a 95% confidence interval for the mean number of people in the 100,000 households was 2.16 < μ < 2.44.

True or false, and explain:

We are 95% confident that the mean number of people in the 625 households is between 2.16 and 2.44.
We are 95% confident that the mean number of people in the 100,000 households is between 2.16 and 2.44.
The probability is 0.95 that the mean number of people in the 100,000 households is between 2.16 and 2.44.
95% of the households in the sample contain between 2.16 and 2.44 people.

a.

Expert Solution

To determine

To explain: Whether the statement “We are 95% confident that the mean number of people in the 625 households is between 2.16 and 2.44 .” is true or false.

Answer to Problem 64E

The given statement “We are 95% confident that the mean number of people in the 625 households is between 2.16 and 2.44 .” is false.

Explanation of Solution

Given:

Out of 100,000 households in a certain city 625 units are randomly selected and the mean number of family members is calculated. The mean was 2.30 and a 95% confidence is defined as 2.16<μ<2.44 .

The confidence interval is constructed for the population mean (μ) ; the mean number of family members in all 100,000 households. Here, the mean number of members in the sample households is already calculated to 2.30 .

Hence, the sample mean is fixed an no need to construct a confidence interval for this statistics.

Conclusion:

Therefore, we can conclude that by the confidence interval the mean of the sample is not defined.

b.

Expert Solution

To determine

To explain: Whether the statement “We are 95% confident that the mean number of people in the 100,000 households is between 2.16 and 2.44 .” is true or false.

Answer to Problem 64E

The statement “We are 95% confident that the mean number of people in the 100,000 households is between 2.16 and 2.44 .” is true.

Explanation of Solution

Out of 100,000 households in a certain city 625 units are randomly selected and the mean number of family members is calculated. The mean was 2.30 and a 95% confidence is defined as 2.16<μ<2.44 .

By the notation μ the population mean is denoted. Hence, the interval 2.76<μ<2.88 with 95% confidence level is to definevariation of population mean.

The population that is discussed in this case is all 100,000 households in the city. therefore, he population mean should be the mean number of members in the total number of households.

Conclusion:

Hence, the mean number of people in the 100,000 households have 95% confidence interval between the given interval.

Conclusion:

Here, in the statement it is said that the 95% confidence interval is for the sample mean. Therefore, this statement is said to be false.

c.

Expert Solution

To determine

To explain: Whether the statement “The probability is 0.95 that the mean GPA of all students in the college is between 2.16 and 2.44 .” is true or false.

Answer to Problem 64E

The statement “The probability is 0.95 that the mean GPA of all students in the college is between 2.16 and 2.44 .” is true.

Explanation of Solution

Out of 100,000 households in a certain city 625 units are randomly selected and the mean number of family members is calculated. The mean was 2.30 and a 95% confidence is defined as 2.16<μ<2.44 .

The confidence level of an interval denotes the chance/ probability of the relevant parameter to be within the interval.

Here, the interval 2.16<μ<2.44 is constructed for the population mean with 95% confidence level. Hence, there is 95% chance that the population mean is between 2.16 and 2.44 .

Generally, a probability is expressed as a decimal or fraction. Hence, we should convert this percentage into a decimal to check the statement.

95%=35100=0.95

Conclusion:

Therefore we can conclude that the probability for the mean number of people in total number of households is between the confidence interval is 0.95 .

d.

Expert Solution

To determine

To explain: Whether the statement “ 95% of the households in the sample contain between 2.16 and 2.44 people.” is true or false.

Answer to Problem 64E

The statement “ 95% of the households in the sample contain between 2.16 and 2.44 people.” is false.

Explanation of Solution

Out of 100,000 households in a certain city 625 units are randomly selected and the mean number of family members is calculated. The mean was 2.30 and a 95% confidence is defined as 2.16<μ<2.44 .

As mentioned in the above parts, the confidence interval is defined for the population mean. Hence all the estimations can be made only for the mean number of people in the total number of households in the city.

In the statement the number of peoples in each household is considered individually. It says there is a 95% chance for the number of people in a randomly selected household to be between 2.16 and 2.44 .

Conclusion:

Therefore, we can conclude that the given confidence interval does not represent a proportion of the population.

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Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

a.

Expert Solution

To determine

To explain: Whether the statement “We are 95% confident that the mean number of people in the 625 households is between 2.16 and 2.44 .” is true or false.

Answer to Problem 64E

The given statement “We are 95% confident that the mean number of people in the 625 households is between 2.16 and 2.44 .” is false.

Explanation of Solution

Given:

Out of 100,000 households in a certain city 625 units are randomly selected and the mean number of family members is calculated. The mean was 2.30 and a 95% confidence is defined as 2.16<μ<2.44 .

The confidence interval is constructed for the population mean (μ) ; the mean number of family members in all 100,000 households. Here, the mean number of members in the sample households is already calculated to 2.30 .

Hence, the sample mean is fixed an no need to construct a confidence interval for this statistics.

Conclusion:

Therefore, we can conclude that by the confidence interval the mean of the sample is not defined.

b.

Expert Solution

To determine

To explain: Whether the statement “We are 95% confident that the mean number of people in the 100,000 households is between 2.16 and 2.44 .” is true or false.

Answer to Problem 64E

The statement “We are 95% confident that the mean number of people in the 100,000 households is between 2.16 and 2.44 .” is true.

Explanation of Solution

Out of 100,000 households in a certain city 625 units are randomly selected and the mean number of family members is calculated. The mean was 2.30 and a 95% confidence is defined as 2.16<μ<2.44 .

By the notation μ the population mean is denoted. Hence, the interval 2.76<μ<2.88 with 95% confidence level is to definevariation of population mean.

The population that is discussed in this case is all 100,000 households in the city. therefore, he population mean should be the mean number of members in the total number of households.

Conclusion:

Hence, the mean number of people in the 100,000 households have 95% confidence interval between the given interval.

Conclusion:

Here, in the statement it is said that the 95% confidence interval is for the sample mean. Therefore, this statement is said to be false.

c.

Expert Solution

To determine

To explain: Whether the statement “The probability is 0.95 that the mean GPA of all students in the college is between 2.16 and 2.44 .” is true or false.

Answer to Problem 64E

The statement “The probability is 0.95 that the mean GPA of all students in the college is between 2.16 and 2.44 .” is true.

Explanation of Solution

Out of 100,000 households in a certain city 625 units are randomly selected and the mean number of family members is calculated. The mean was 2.30 and a 95% confidence is defined as 2.16<μ<2.44 .

The confidence level of an interval denotes the chance/ probability of the relevant parameter to be within the interval.

Here, the interval 2.16<μ<2.44 is constructed for the population mean with 95% confidence level. Hence, there is 95% chance that the population mean is between 2.16 and 2.44 .

Generally, a probability is expressed as a decimal or fraction. Hence, we should convert this percentage into a decimal to check the statement.

95%=35100=0.95

Conclusion:

Therefore we can conclude that the probability for the mean number of people in total number of households is between the confidence interval is 0.95 .

d.

Expert Solution

To determine

To explain: Whether the statement “ 95% of the households in the sample contain between 2.16 and 2.44 people.” is true or false.

Answer to Problem 64E

The statement “ 95% of the households in the sample contain between 2.16 and 2.44 people.” is false.

Explanation of Solution

Out of 100,000 households in a certain city 625 units are randomly selected and the mean number of family members is calculated. The mean was 2.30 and a 95% confidence is defined as 2.16<μ<2.44 .

As mentioned in the above parts, the confidence interval is defined for the population mean. Hence all the estimations can be made only for the mean number of people in the total number of households in the city.

In the statement the number of peoples in each household is considered individually. It says there is a 95% chance for the number of people in a randomly selected household to be between 2.16 and 2.44 .

Conclusion:

Therefore, we can conclude that the given confidence interval does not represent a proportion of the population.

Answer 8

a.

Expert Solution

To determine

To explain: Whether the statement “We are 95% confident that the mean number of people in the 625 households is between 2.16 and 2.44 .” is true or false.

Answer to Problem 64E

The given statement “We are 95% confident that the mean number of people in the 625 households is between 2.16 and 2.44 .” is false.

Explanation of Solution

Given:

Out of 100,000 households in a certain city 625 units are randomly selected and the mean number of family members is calculated. The mean was 2.30 and a 95% confidence is defined as 2.16<μ<2.44 .

The confidence interval is constructed for the population mean (μ) ; the mean number of family members in all 100,000 households. Here, the mean number of members in the sample households is already calculated to 2.30 .

Hence, the sample mean is fixed an no need to construct a confidence interval for this statistics.

Conclusion:

Therefore, we can conclude that by the confidence interval the mean of the sample is not defined.

Answer 9

a.

Expert Solution

Answer 10

a.

Expert Solution

Answer 11

Expert Solution

Answer 12

To determine

To explain: Whether the statement “We are 95% confident that the mean number of people in the 625 households is between 2.16 and 2.44 .” is true or false.

Answer 13

Answer to Problem 64E

The given statement “We are 95% confident that the mean number of people in the 625 households is between 2.16 and 2.44 .” is false.

Answer 14

Explanation of Solution

Given:

Out of 100,000 households in a certain city 625 units are randomly selected and the mean number of family members is calculated. The mean was 2.30 and a 95% confidence is defined as 2.16<μ<2.44 .

The confidence interval is constructed for the population mean (μ) ; the mean number of family members in all 100,000 households. Here, the mean number of members in the sample households is already calculated to 2.30 .

Hence, the sample mean is fixed an no need to construct a confidence interval for this statistics.

Conclusion:

Therefore, we can conclude that by the confidence interval the mean of the sample is not defined.

Answer 15

b.

Expert Solution

To determine

To explain: Whether the statement “We are 95% confident that the mean number of people in the 100,000 households is between 2.16 and 2.44 .” is true or false.

Answer to Problem 64E

The statement “We are 95% confident that the mean number of people in the 100,000 households is between 2.16 and 2.44 .” is true.

Explanation of Solution

Out of 100,000 households in a certain city 625 units are randomly selected and the mean number of family members is calculated. The mean was 2.30 and a 95% confidence is defined as 2.16<μ<2.44 .

By the notation μ the population mean is denoted. Hence, the interval 2.76<μ<2.88 with 95% confidence level is to definevariation of population mean.

The population that is discussed in this case is all 100,000 households in the city. therefore, he population mean should be the mean number of members in the total number of households.

Conclusion:

Hence, the mean number of people in the 100,000 households have 95% confidence interval between the given interval.

Conclusion:

Here, in the statement it is said that the 95% confidence interval is for the sample mean. Therefore, this statement is said to be false.

Answer 16

b.

Expert Solution

Answer 17

b.

Expert Solution

Answer 18

Expert Solution

Answer 19

To determine

To explain: Whether the statement “We are 95% confident that the mean number of people in the 100,000 households is between 2.16 and 2.44 .” is true or false.

Answer 20

Answer to Problem 64E

The statement “We are 95% confident that the mean number of people in the 100,000 households is between 2.16 and 2.44 .” is true.

Answer 21

Explanation of Solution

Out of 100,000 households in a certain city 625 units are randomly selected and the mean number of family members is calculated. The mean was 2.30 and a 95% confidence is defined as 2.16<μ<2.44 .

By the notation μ the population mean is denoted. Hence, the interval 2.76<μ<2.88 with 95% confidence level is to definevariation of population mean.

The population that is discussed in this case is all 100,000 households in the city. therefore, he population mean should be the mean number of members in the total number of households.

Conclusion:

Hence, the mean number of people in the 100,000 households have 95% confidence interval between the given interval.

Conclusion:

Here, in the statement it is said that the 95% confidence interval is for the sample mean. Therefore, this statement is said to be false.

Answer 22

c.

Expert Solution

To determine

To explain: Whether the statement “The probability is 0.95 that the mean GPA of all students in the college is between 2.16 and 2.44 .” is true or false.

Answer to Problem 64E

The statement “The probability is 0.95 that the mean GPA of all students in the college is between 2.16 and 2.44 .” is true.

Explanation of Solution

Out of 100,000 households in a certain city 625 units are randomly selected and the mean number of family members is calculated. The mean was 2.30 and a 95% confidence is defined as 2.16<μ<2.44 .

The confidence level of an interval denotes the chance/ probability of the relevant parameter to be within the interval.

Here, the interval 2.16<μ<2.44 is constructed for the population mean with 95% confidence level. Hence, there is 95% chance that the population mean is between 2.16 and 2.44 .

Generally, a probability is expressed as a decimal or fraction. Hence, we should convert this percentage into a decimal to check the statement.

95%=35100=0.95

Conclusion:

Therefore we can conclude that the probability for the mean number of people in total number of households is between the confidence interval is 0.95 .

Answer 23

c.

Expert Solution

Answer 24

c.

Expert Solution

Answer 25

Expert Solution

Answer 26

To determine

To explain: Whether the statement “The probability is 0.95 that the mean GPA of all students in the college is between 2.16 and 2.44 .” is true or false.

Answer 27

Answer to Problem 64E

The statement “The probability is 0.95 that the mean GPA of all students in the college is between 2.16 and 2.44 .” is true.

Answer 28

Explanation of Solution

Out of 100,000 households in a certain city 625 units are randomly selected and the mean number of family members is calculated. The mean was 2.30 and a 95% confidence is defined as 2.16<μ<2.44 .

The confidence level of an interval denotes the chance/ probability of the relevant parameter to be within the interval.

Here, the interval 2.16<μ<2.44 is constructed for the population mean with 95% confidence level. Hence, there is 95% chance that the population mean is between 2.16 and 2.44 .

Generally, a probability is expressed as a decimal or fraction. Hence, we should convert this percentage into a decimal to check the statement.

95%=35100=0.95

Conclusion:

Therefore we can conclude that the probability for the mean number of people in total number of households is between the confidence interval is 0.95 .

Answer 29

d.

Expert Solution

To determine

To explain: Whether the statement “ 95% of the households in the sample contain between 2.16 and 2.44 people.” is true or false.

Answer to Problem 64E

The statement “ 95% of the households in the sample contain between 2.16 and 2.44 people.” is false.

Explanation of Solution

Out of 100,000 households in a certain city 625 units are randomly selected and the mean number of family members is calculated. The mean was 2.30 and a 95% confidence is defined as 2.16<μ<2.44 .

As mentioned in the above parts, the confidence interval is defined for the population mean. Hence all the estimations can be made only for the mean number of people in the total number of households in the city.

In the statement the number of peoples in each household is considered individually. It says there is a 95% chance for the number of people in a randomly selected household to be between 2.16 and 2.44 .

Conclusion:

Therefore, we can conclude that the given confidence interval does not represent a proportion of the population.

Answer 30

d.

Expert Solution

Answer 31

d.

Expert Solution

Answer 32

Expert Solution

Answer 33

To determine

To explain: Whether the statement “ 95% of the households in the sample contain between 2.16 and 2.44 people.” is true or false.

Answer 34

Answer to Problem 64E

The statement “ 95% of the households in the sample contain between 2.16 and 2.44 people.” is false.

Answer 35

Explanation of Solution

Out of 100,000 households in a certain city 625 units are randomly selected and the mean number of family members is calculated. The mean was 2.30 and a 95% confidence is defined as 2.16<μ<2.44 .

As mentioned in the above parts, the confidence interval is defined for the population mean. Hence all the estimations can be made only for the mean number of people in the total number of households in the city.

In the statement the number of peoples in each household is considered individually. It says there is a 95% chance for the number of people in a randomly selected household to be between 2.16 and 2.44 .

Conclusion:

Therefore, we can conclude that the given confidence interval does not represent a proportion of the population.