Construct a 1 − α confidence interval for μ from the sample data. Find the value of μ in the null hypothesis. Identify whether the value of μ is in the confidence interval not. Check whether the null hypothesis is rejecting or fail to reject by using the confidence interval method.

Question

You assume that the annual incomes for certain workers are normal with a mean of $28,500 and a standard deviation of $2,400. What’s the chance that a randomly selected employee makes more than $30,000?What’s the chance that 36 randomly selected employees make more than $30,000, on average?

Answer 1

Question

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Chapter 8.2, Problem 26P

(a)

To determine

Construct a 1−α confidence interval for μ from the sample data.

Find the value of μ in the null hypothesis.

Identify whether the value of μ is in the confidence interval not.

Check whether the null hypothesis is rejecting or fail to reject by using the confidence interval method.

(b)

To determine

Find the P-value for the test.

Check whether the null hypothesis is rejecting or fail to reject.

Compare the results with the part (a).

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You assume that the annual incomes for certain workers are normal with a mean of $28,500 and a standard deviation of $2,400. What’s the chance that a randomly selected employee makes more than $30,000?What’s the chance that 36 randomly selected employees make more than $30,000, on average?

What’s the chance that a fair coin comes up heads more than 60 times when you toss it 100 times?

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Answer 2

Question

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Chapter 8.2, Problem 26P

(a)

To determine

Construct a 1−α confidence interval for μ from the sample data.

Find the value of μ in the null hypothesis.

Identify whether the value of μ is in the confidence interval not.

Check whether the null hypothesis is rejecting or fail to reject by using the confidence interval method.

(b)

To determine

Find the P-value for the test.

Check whether the null hypothesis is rejecting or fail to reject.

Compare the results with the part (a).

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Answer 3

Question

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Chapter 8.2, Problem 26P

(a)

To determine

Construct a 1−α confidence interval for μ from the sample data.

Find the value of μ in the null hypothesis.

Identify whether the value of μ is in the confidence interval not.

Check whether the null hypothesis is rejecting or fail to reject by using the confidence interval method.

(b)

To determine

Find the P-value for the test.

Check whether the null hypothesis is rejecting or fail to reject.

Compare the results with the part (a).

Expert Solution & Answer

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Answer 4

Question

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Chapter 8.2, Problem 26P

(a)

To determine

Construct a 1−α confidence interval for μ from the sample data.

Find the value of μ in the null hypothesis.

Identify whether the value of μ is in the confidence interval not.

Check whether the null hypothesis is rejecting or fail to reject by using the confidence interval method.

(b)

To determine

Find the P-value for the test.

Check whether the null hypothesis is rejecting or fail to reject.

Compare the results with the part (a).

Expert Solution & Answer

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Answer 5

Chapter 8.2, Problem 26P

(a)

To determine

Construct a 1−α confidence interval for μ from the sample data.

Find the value of μ in the null hypothesis.

Identify whether the value of μ is in the confidence interval not.

Check whether the null hypothesis is rejecting or fail to reject by using the confidence interval method.

(b)

To determine

Find the P-value for the test.

Check whether the null hypothesis is rejecting or fail to reject.

Compare the results with the part (a).

Answer 6

Chapter 8.2, Problem 26P

(a)

To determine

Construct a 1−α confidence interval for μ from the sample data.

Find the value of μ in the null hypothesis.

Identify whether the value of μ is in the confidence interval not.

Check whether the null hypothesis is rejecting or fail to reject by using the confidence interval method.

Answer 7

Chapter 8.2, Problem 26P

(a)

To determine

Construct a 1−α confidence interval for μ from the sample data.

Find the value of μ in the null hypothesis.

Identify whether the value of μ is in the confidence interval not.

Check whether the null hypothesis is rejecting or fail to reject by using the confidence interval method.

Answer 8

(b)

To determine

Find the P-value for the test.

Check whether the null hypothesis is rejecting or fail to reject.

Compare the results with the part (a).

Answer 9

(b)

To determine

Find the P-value for the test.

Check whether the null hypothesis is rejecting or fail to reject.

Compare the results with the part (a).

Answer 10

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Answer 21

Construct a 1 − α confidence interval for μ from the sample data. Find the value of μ in the null hypothesis. Identify whether the value of μ is in the confidence interval not. Check whether the null hypothesis is rejecting or fail to reject by using the confidence interval method.

Solution Summary: The author constructs a 1-alpha confidence interval for mu from the sample data.

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Construct a 1−α confidence interval for μ from the sample data.

Find the value of μ in the null hypothesis.

Identify whether the value of μ is in the confidence interval not.

Check whether the null hypothesis is rejecting or fail to reject by using the confidence interval method.

Find the P-value for the test.

Check whether the null hypothesis is rejecting or fail to reject.

Compare the results with the part (a).

Chapter 8 Solutions

Construct a 1 − α confidence interval for μ from the sample data. Find the value of μ in the null hypothesis. Identify whether the value of μ is in the confidence interval not. Check whether the null hypothesis is rejecting or fail to reject by using the confidence interval method.

Solution Summary: The author constructs a 1-alpha confidence interval for mu from the sample data.

Videos

Construct a 1−α confidence interval for μ from the sample data. Find the value of μ in the null hypothesis. Identify whether the value of μ is in the confidence interval not. Check whether the null hypothesis is rejecting or fail to reject by using the confidence interval method.

Find the P-value for the test. Check whether the null hypothesis is rejecting or fail to reject. Compare the results with the part (a).

Chapter 8 Solutions

Construct a 1−α confidence interval for μ from the sample data.

Find the value of μ in the null hypothesis.

Identify whether the value of μ is in the confidence interval not.

Check whether the null hypothesis is rejecting or fail to reject by using the confidence interval method.

Find the P-value for the test.

Check whether the null hypothesis is rejecting or fail to reject.

Compare the results with the part (a).