Obtain the margin of error for the proportion of all adult Wisconsin residents thinking that things are going in the wrong direction for 90% confidence.

Question

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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 18, Problem 5E

a.

To determine

Obtain the margin of error for the proportion of all adult Wisconsin residents thinking that things are going in the wrong direction for 90% confidence.

a.

Expert Solution

Answer to Problem 5E

The margin of error for the proportion of all adult Wisconsin residents who think things are going in the wrong direction for 90% confidence is 0.039 or 3.9%.

Explanation of Solution

Calculation:

The survey conducted by St. Norbert’s College in Green Bay, Wisconsin and Wisconsin Public Radio on the sample of 402 Wisconsin resident adults, 66% said that things in the country are going in the wrong direction.

Margin of error:

The margin of error for the estimate of proportion, p is,

ME=z*×p^q^n

Where, z* denotes critical value from the standard normal distribution, n be the number of samples, p^ be the sample proportion and q^=1−p^.

Critical value for 90% confidence:

Software Procedure:

Step-by-step procedure to obtain the critical value using the MINITAB software:

Choose Graph > Probability Distribution Plot choose View Probability > OK.
From Distribution, choose ‘Normal’ distribution.
Enter Mean as 0.0 and standard deviation as 1.0.
Click the Shaded Area tab.
Choose Probability Value and Both Tail for the region of the curve to shade.
Enter the Probability as 0.10.
Click OK.

Output using the MINITAB software is given below:

STATS:DATA+MODELS-W/DVD, Chapter 18, Problem 5E , additional homework tip 1

From the MINITAB output, the critical values at 90% confidence are z*=±1.645.

The margin of error is:

Substitute z as 1.645, p^ as 0.66 and q^ as 0.34 (=1−p^) and n as 402 in the formula,

ME=1.645×(0.66)(0.34)402=1.645×0.2244402=1.645×0.02363≈0.039

Thus, the margin of error for the proportion of all adult Wisconsin residents who think things are going in the wrong direction for 90% confidence is 0.039 or 3.9%.

b.

To determine

Explain whether the margin of error is larger or smaller for 95% confidence.

b.

Expert Solution

Answer to Problem 5E

The margin of error is larger for 95% confidence.

Explanation of Solution

Justification:

Critical value for 95% confidence:

Software Procedure:

Step-by-step procedure to obtain the critical value using the MINITAB software:

Choose Graph > Probability Distribution Plot choose View Probability > OK.
From Distribution, choose ‘Normal’ distribution.
Enter Mean as 0.0 and standard deviation as 1.0.
Click the Shaded Area tab.
Choose Probability Value and Both Tail for the region of the curve to shade.
Enter the Probability as 0.05.
Click OK.

Output using the MINITAB software is given below:

STATS:DATA+MODELS-W/DVD, Chapter 18, Problem 5E , additional homework tip 2

From the MINITAB output, the critical values at 95% confidence are z*=±1.96.

For this particular problem, the values of n, p^ and q^ are constant. As a result, the margin of error depends only upon the critical value z*. The margin of error increases with the increase in z*.

The critical value for 95% confidence is 1.96 which is greater than the critical value 1.645 of 90% confidence.

Therefore, the margin of error for 95% confidence is larger than that obtained for the 90% confidence.

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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 18, Problem 5E

a.

To determine

Obtain the margin of error for the proportion of all adult Wisconsin residents thinking that things are going in the wrong direction for 90% confidence.

a.

Expert Solution

Answer to Problem 5E

The margin of error for the proportion of all adult Wisconsin residents who think things are going in the wrong direction for 90% confidence is 0.039 or 3.9%.

Explanation of Solution

Calculation:

The survey conducted by St. Norbert’s College in Green Bay, Wisconsin and Wisconsin Public Radio on the sample of 402 Wisconsin resident adults, 66% said that things in the country are going in the wrong direction.

Margin of error:

The margin of error for the estimate of proportion, p is,

ME=z*×p^q^n

Where, z* denotes critical value from the standard normal distribution, n be the number of samples, p^ be the sample proportion and q^=1−p^.

Critical value for 90% confidence:

Software Procedure:

Step-by-step procedure to obtain the critical value using the MINITAB software:

Choose Graph > Probability Distribution Plot choose View Probability > OK.
From Distribution, choose ‘Normal’ distribution.
Enter Mean as 0.0 and standard deviation as 1.0.
Click the Shaded Area tab.
Choose Probability Value and Both Tail for the region of the curve to shade.
Enter the Probability as 0.10.
Click OK.

Output using the MINITAB software is given below:

STATS:DATA+MODELS-W/DVD, Chapter 18, Problem 5E , additional homework tip 1

From the MINITAB output, the critical values at 90% confidence are z*=±1.645.

The margin of error is:

Substitute z as 1.645, p^ as 0.66 and q^ as 0.34 (=1−p^) and n as 402 in the formula,

ME=1.645×(0.66)(0.34)402=1.645×0.2244402=1.645×0.02363≈0.039

Thus, the margin of error for the proportion of all adult Wisconsin residents who think things are going in the wrong direction for 90% confidence is 0.039 or 3.9%.

b.

To determine

Explain whether the margin of error is larger or smaller for 95% confidence.

b.

Expert Solution

Answer to Problem 5E

The margin of error is larger for 95% confidence.

Explanation of Solution

Justification:

Critical value for 95% confidence:

Software Procedure:

Step-by-step procedure to obtain the critical value using the MINITAB software:

Choose Graph > Probability Distribution Plot choose View Probability > OK.
From Distribution, choose ‘Normal’ distribution.
Enter Mean as 0.0 and standard deviation as 1.0.
Click the Shaded Area tab.
Choose Probability Value and Both Tail for the region of the curve to shade.
Enter the Probability as 0.05.
Click OK.

Output using the MINITAB software is given below:

STATS:DATA+MODELS-W/DVD, Chapter 18, Problem 5E , additional homework tip 2

From the MINITAB output, the critical values at 95% confidence are z*=±1.96.

For this particular problem, the values of n, p^ and q^ are constant. As a result, the margin of error depends only upon the critical value z*. The margin of error increases with the increase in z*.

The critical value for 95% confidence is 1.96 which is greater than the critical value 1.645 of 90% confidence.

Therefore, the margin of error for 95% confidence is larger than that obtained for the 90% confidence.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

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 18, Problem 5E

a.

To determine

Obtain the margin of error for the proportion of all adult Wisconsin residents thinking that things are going in the wrong direction for 90% confidence.

a.

Expert Solution

Answer to Problem 5E

The margin of error for the proportion of all adult Wisconsin residents who think things are going in the wrong direction for 90% confidence is 0.039 or 3.9%.

Explanation of Solution

Calculation:

The survey conducted by St. Norbert’s College in Green Bay, Wisconsin and Wisconsin Public Radio on the sample of 402 Wisconsin resident adults, 66% said that things in the country are going in the wrong direction.

Margin of error:

The margin of error for the estimate of proportion, p is,

ME=z*×p^q^n

Where, z* denotes critical value from the standard normal distribution, n be the number of samples, p^ be the sample proportion and q^=1−p^.

Critical value for 90% confidence:

Software Procedure:

Step-by-step procedure to obtain the critical value using the MINITAB software:

Choose Graph > Probability Distribution Plot choose View Probability > OK.
From Distribution, choose ‘Normal’ distribution.
Enter Mean as 0.0 and standard deviation as 1.0.
Click the Shaded Area tab.
Choose Probability Value and Both Tail for the region of the curve to shade.
Enter the Probability as 0.10.
Click OK.

Output using the MINITAB software is given below:

STATS:DATA+MODELS-W/DVD, Chapter 18, Problem 5E , additional homework tip 1

From the MINITAB output, the critical values at 90% confidence are z*=±1.645.

The margin of error is:

Substitute z as 1.645, p^ as 0.66 and q^ as 0.34 (=1−p^) and n as 402 in the formula,

ME=1.645×(0.66)(0.34)402=1.645×0.2244402=1.645×0.02363≈0.039

Thus, the margin of error for the proportion of all adult Wisconsin residents who think things are going in the wrong direction for 90% confidence is 0.039 or 3.9%.

b.

To determine

Explain whether the margin of error is larger or smaller for 95% confidence.

b.

Expert Solution

Answer to Problem 5E

The margin of error is larger for 95% confidence.

Explanation of Solution

Justification:

Critical value for 95% confidence:

Software Procedure:

Step-by-step procedure to obtain the critical value using the MINITAB software:

Choose Graph > Probability Distribution Plot choose View Probability > OK.
From Distribution, choose ‘Normal’ distribution.
Enter Mean as 0.0 and standard deviation as 1.0.
Click the Shaded Area tab.
Choose Probability Value and Both Tail for the region of the curve to shade.
Enter the Probability as 0.05.
Click OK.

Output using the MINITAB software is given below:

STATS:DATA+MODELS-W/DVD, Chapter 18, Problem 5E , additional homework tip 2

From the MINITAB output, the critical values at 95% confidence are z*=±1.96.

For this particular problem, the values of n, p^ and q^ are constant. As a result, the margin of error depends only upon the critical value z*. The margin of error increases with the increase in z*.

The critical value for 95% confidence is 1.96 which is greater than the critical value 1.645 of 90% confidence.

Therefore, the margin of error for 95% confidence is larger than that obtained for the 90% confidence.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

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 18, Problem 5E

a.

To determine

Obtain the margin of error for the proportion of all adult Wisconsin residents thinking that things are going in the wrong direction for 90% confidence.

a.

Expert Solution

Answer to Problem 5E

The margin of error for the proportion of all adult Wisconsin residents who think things are going in the wrong direction for 90% confidence is 0.039 or 3.9%.

Explanation of Solution

Calculation:

The survey conducted by St. Norbert’s College in Green Bay, Wisconsin and Wisconsin Public Radio on the sample of 402 Wisconsin resident adults, 66% said that things in the country are going in the wrong direction.

Margin of error:

The margin of error for the estimate of proportion, p is,

ME=z*×p^q^n

Where, z* denotes critical value from the standard normal distribution, n be the number of samples, p^ be the sample proportion and q^=1−p^.

Critical value for 90% confidence:

Software Procedure:

Step-by-step procedure to obtain the critical value using the MINITAB software:

Choose Graph > Probability Distribution Plot choose View Probability > OK.
From Distribution, choose ‘Normal’ distribution.
Enter Mean as 0.0 and standard deviation as 1.0.
Click the Shaded Area tab.
Choose Probability Value and Both Tail for the region of the curve to shade.
Enter the Probability as 0.10.
Click OK.

Output using the MINITAB software is given below:

STATS:DATA+MODELS-W/DVD, Chapter 18, Problem 5E , additional homework tip 1

From the MINITAB output, the critical values at 90% confidence are z*=±1.645.

The margin of error is:

Substitute z as 1.645, p^ as 0.66 and q^ as 0.34 (=1−p^) and n as 402 in the formula,

ME=1.645×(0.66)(0.34)402=1.645×0.2244402=1.645×0.02363≈0.039

Thus, the margin of error for the proportion of all adult Wisconsin residents who think things are going in the wrong direction for 90% confidence is 0.039 or 3.9%.

b.

To determine

Explain whether the margin of error is larger or smaller for 95% confidence.

b.

Expert Solution

Answer to Problem 5E

The margin of error is larger for 95% confidence.

Explanation of Solution

Justification:

Critical value for 95% confidence:

Software Procedure:

Step-by-step procedure to obtain the critical value using the MINITAB software:

Choose Graph > Probability Distribution Plot choose View Probability > OK.
From Distribution, choose ‘Normal’ distribution.
Enter Mean as 0.0 and standard deviation as 1.0.
Click the Shaded Area tab.
Choose Probability Value and Both Tail for the region of the curve to shade.
Enter the Probability as 0.05.
Click OK.

Output using the MINITAB software is given below:

STATS:DATA+MODELS-W/DVD, Chapter 18, Problem 5E , additional homework tip 2

From the MINITAB output, the critical values at 95% confidence are z*=±1.96.

For this particular problem, the values of n, p^ and q^ are constant. As a result, the margin of error depends only upon the critical value z*. The margin of error increases with the increase in z*.

The critical value for 95% confidence is 1.96 which is greater than the critical value 1.645 of 90% confidence.

Therefore, the margin of error for 95% confidence is larger than that obtained for the 90% confidence.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Chapter 18, Problem 5E

a.

To determine

Obtain the margin of error for the proportion of all adult Wisconsin residents thinking that things are going in the wrong direction for 90% confidence.

a.

Expert Solution

Answer to Problem 5E

The margin of error for the proportion of all adult Wisconsin residents who think things are going in the wrong direction for 90% confidence is 0.039 or 3.9%.

Explanation of Solution

Calculation:

The survey conducted by St. Norbert’s College in Green Bay, Wisconsin and Wisconsin Public Radio on the sample of 402 Wisconsin resident adults, 66% said that things in the country are going in the wrong direction.

Margin of error:

The margin of error for the estimate of proportion, p is,

ME=z*×p^q^n

Where, z* denotes critical value from the standard normal distribution, n be the number of samples, p^ be the sample proportion and q^=1−p^.

Critical value for 90% confidence:

Software Procedure:

Step-by-step procedure to obtain the critical value using the MINITAB software:

Choose Graph > Probability Distribution Plot choose View Probability > OK.
From Distribution, choose ‘Normal’ distribution.
Enter Mean as 0.0 and standard deviation as 1.0.
Click the Shaded Area tab.
Choose Probability Value and Both Tail for the region of the curve to shade.
Enter the Probability as 0.10.
Click OK.

Output using the MINITAB software is given below:

STATS:DATA+MODELS-W/DVD, Chapter 18, Problem 5E , additional homework tip 1

From the MINITAB output, the critical values at 90% confidence are z*=±1.645.

The margin of error is:

Substitute z as 1.645, p^ as 0.66 and q^ as 0.34 (=1−p^) and n as 402 in the formula,

ME=1.645×(0.66)(0.34)402=1.645×0.2244402=1.645×0.02363≈0.039

Thus, the margin of error for the proportion of all adult Wisconsin residents who think things are going in the wrong direction for 90% confidence is 0.039 or 3.9%.

b.

To determine

Explain whether the margin of error is larger or smaller for 95% confidence.

b.

Expert Solution

Answer to Problem 5E

The margin of error is larger for 95% confidence.

Explanation of Solution

Justification:

Critical value for 95% confidence:

Software Procedure:

Step-by-step procedure to obtain the critical value using the MINITAB software:

Choose Graph > Probability Distribution Plot choose View Probability > OK.
From Distribution, choose ‘Normal’ distribution.
Enter Mean as 0.0 and standard deviation as 1.0.
Click the Shaded Area tab.
Choose Probability Value and Both Tail for the region of the curve to shade.
Enter the Probability as 0.05.
Click OK.

Output using the MINITAB software is given below:

STATS:DATA+MODELS-W/DVD, Chapter 18, Problem 5E , additional homework tip 2

From the MINITAB output, the critical values at 95% confidence are z*=±1.96.

For this particular problem, the values of n, p^ and q^ are constant. As a result, the margin of error depends only upon the critical value z*. The margin of error increases with the increase in z*.

The critical value for 95% confidence is 1.96 which is greater than the critical value 1.645 of 90% confidence.

Therefore, the margin of error for 95% confidence is larger than that obtained for the 90% confidence.

Answer 6

Chapter 18, Problem 5E

a.

To determine

Obtain the margin of error for the proportion of all adult Wisconsin residents thinking that things are going in the wrong direction for 90% confidence.

a.

Expert Solution

Answer to Problem 5E

The margin of error for the proportion of all adult Wisconsin residents who think things are going in the wrong direction for 90% confidence is 0.039 or 3.9%.

Explanation of Solution

Calculation:

The survey conducted by St. Norbert’s College in Green Bay, Wisconsin and Wisconsin Public Radio on the sample of 402 Wisconsin resident adults, 66% said that things in the country are going in the wrong direction.

Margin of error:

The margin of error for the estimate of proportion, p is,

ME=z*×p^q^n

Where, z* denotes critical value from the standard normal distribution, n be the number of samples, p^ be the sample proportion and q^=1−p^.

Critical value for 90% confidence:

Software Procedure:

Step-by-step procedure to obtain the critical value using the MINITAB software:

Choose Graph > Probability Distribution Plot choose View Probability > OK.
From Distribution, choose ‘Normal’ distribution.
Enter Mean as 0.0 and standard deviation as 1.0.
Click the Shaded Area tab.
Choose Probability Value and Both Tail for the region of the curve to shade.
Enter the Probability as 0.10.
Click OK.

Output using the MINITAB software is given below:

STATS:DATA+MODELS-W/DVD, Chapter 18, Problem 5E , additional homework tip 1

From the MINITAB output, the critical values at 90% confidence are z*=±1.645.

The margin of error is:

Substitute z as 1.645, p^ as 0.66 and q^ as 0.34 (=1−p^) and n as 402 in the formula,

ME=1.645×(0.66)(0.34)402=1.645×0.2244402=1.645×0.02363≈0.039

Thus, the margin of error for the proportion of all adult Wisconsin residents who think things are going in the wrong direction for 90% confidence is 0.039 or 3.9%.

Answer 7

Chapter 18, Problem 5E

a.

To determine

Obtain the margin of error for the proportion of all adult Wisconsin residents thinking that things are going in the wrong direction for 90% confidence.

Answer 8

a.

Expert Solution

Answer to Problem 5E

The margin of error for the proportion of all adult Wisconsin residents who think things are going in the wrong direction for 90% confidence is 0.039 or 3.9%.

Answer 9

a.

Expert Solution

Answer 10

a.

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

Calculation:

The survey conducted by St. Norbert’s College in Green Bay, Wisconsin and Wisconsin Public Radio on the sample of 402 Wisconsin resident adults, 66% said that things in the country are going in the wrong direction.

Margin of error:

The margin of error for the estimate of proportion, p is,

ME=z*×p^q^n

Where, z* denotes critical value from the standard normal distribution, n be the number of samples, p^ be the sample proportion and q^=1−p^.

Critical value for 90% confidence:

Software Procedure:

Step-by-step procedure to obtain the critical value using the MINITAB software:

Choose Graph > Probability Distribution Plot choose View Probability > OK.
From Distribution, choose ‘Normal’ distribution.
Enter Mean as 0.0 and standard deviation as 1.0.
Click the Shaded Area tab.
Choose Probability Value and Both Tail for the region of the curve to shade.
Enter the Probability as 0.10.
Click OK.

Output using the MINITAB software is given below:

STATS:DATA+MODELS-W/DVD, Chapter 18, Problem 5E , additional homework tip 1

From the MINITAB output, the critical values at 90% confidence are z*=±1.645.

The margin of error is:

Substitute z as 1.645, p^ as 0.66 and q^ as 0.34 (=1−p^) and n as 402 in the formula,

ME=1.645×(0.66)(0.34)402=1.645×0.2244402=1.645×0.02363≈0.039

Thus, the margin of error for the proportion of all adult Wisconsin residents who think things are going in the wrong direction for 90% confidence is 0.039 or 3.9%.

Answer 13

b.

To determine

Explain whether the margin of error is larger or smaller for 95% confidence.

b.

Expert Solution

Answer to Problem 5E

The margin of error is larger for 95% confidence.

Explanation of Solution

Justification:

Critical value for 95% confidence:

Software Procedure:

Step-by-step procedure to obtain the critical value using the MINITAB software:

Choose Graph > Probability Distribution Plot choose View Probability > OK.
From Distribution, choose ‘Normal’ distribution.
Enter Mean as 0.0 and standard deviation as 1.0.
Click the Shaded Area tab.
Choose Probability Value and Both Tail for the region of the curve to shade.
Enter the Probability as 0.05.
Click OK.

Output using the MINITAB software is given below:

STATS:DATA+MODELS-W/DVD, Chapter 18, Problem 5E , additional homework tip 2

From the MINITAB output, the critical values at 95% confidence are z*=±1.96.

For this particular problem, the values of n, p^ and q^ are constant. As a result, the margin of error depends only upon the critical value z*. The margin of error increases with the increase in z*.

The critical value for 95% confidence is 1.96 which is greater than the critical value 1.645 of 90% confidence.

Therefore, the margin of error for 95% confidence is larger than that obtained for the 90% confidence.

Answer 14

b.

To determine

Explain whether the margin of error is larger or smaller for 95% confidence.

Answer 15

b.

Expert Solution

Answer to Problem 5E

The margin of error is larger for 95% confidence.

Answer 16

b.

Expert Solution

Answer 17

b.

Expert Solution

Answer 18

Expert Solution

Answer 19

Explanation of Solution

Justification:

Critical value for 95% confidence:

Software Procedure:

Step-by-step procedure to obtain the critical value using the MINITAB software:

Choose Graph > Probability Distribution Plot choose View Probability > OK.
From Distribution, choose ‘Normal’ distribution.
Enter Mean as 0.0 and standard deviation as 1.0.
Click the Shaded Area tab.
Choose Probability Value and Both Tail for the region of the curve to shade.
Enter the Probability as 0.05.
Click OK.

Output using the MINITAB software is given below:

STATS:DATA+MODELS-W/DVD, Chapter 18, Problem 5E , additional homework tip 2

From the MINITAB output, the critical values at 95% confidence are z*=±1.96.

For this particular problem, the values of n, p^ and q^ are constant. As a result, the margin of error depends only upon the critical value z*. The margin of error increases with the increase in z*.

The critical value for 95% confidence is 1.96 which is greater than the critical value 1.645 of 90% confidence.

Therefore, the margin of error for 95% confidence is larger than that obtained for the 90% confidence.

Answer 20

Ch. 18.1 - Prob. 1JC Ch. 18.1 - Prob. 2JC Ch. 18.1 - Prob. 3JC Ch. 18.1 - Prob. 4JC Ch. 18.1 - Prob. 5JC Ch. 18.3 - Prob. 6JC Ch. 18.3 - Prob. 7JC Ch. 18.3 - Think some more about the 95% confidence interval...Ch. 18 - Prob. 5E Ch. 18 - Prob. 37E

Obtain the margin of error for the proportion of all adult Wisconsin residents thinking that things are going in the wrong direction for 90% confidence.

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Obtain the margin of error for the proportion of all adult Wisconsin residents thinking that things are going in the wrong direction for 90% confidence.

Answer to Problem 5E

Explanation of Solution

Explain whether the margin of error is larger or smaller for 95% confidence.

Answer to Problem 5E

Explanation of Solution

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