The critical value of t at the confidence level of 99%.

Question

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Answer 1

Question

Chapter 9, Problem 1RE

(a)

To determine

The critical value of t at the confidence level of 99%.

(a)

Expert Solution

Answer to Problem 1RE

Solution: The critical value of t at 99% level of confidence for the sample size of n=18 is t0.005=2.898_.

Explanation of Solution

Given: The alpha is 0.01 and the size of the sample is n=18.

Explanation: For 99% confidence level, the confidence interval has 0.5% for its greater-than probability and 0.5% for its less-than probability. Hence, the required area is in the right tail of 0.005. Since the sample size is n=18, the degrees of freedom are 18−1=17.

Obtain the critical value of t by using the distribution table of the t-test. Then, look for 17 degrees of freedom in the row and 1% level of significance in the column. The required t-value is the value that intersects this row and column.

The critical value of t with 17 degrees of freedom is obtained as 2.898 from the table.

(b)

To determine

The critical value of t at 90% level of confidence.

(b)

Expert Solution

Answer to Problem 1RE

Solution: The critical value of t at 90% level of confidence for the sample size of n=27 is t0.05=1.706_.

Explanation of Solution

Given: The alpha is 0.1 and the size of the sample is n=27.

Explanation: For 90% confidence level, the confidence interval has 5% for its greater-than probability and 5% for its less-than probability. Hence, the required area is in the right tail of 0.05. Since the sample size is n=27, the degrees of freedom are 27−1=26.

Obtain the critical value of t by using the distribution table of the t-test. Then, look for 26 degrees of freedom in the row and 10% level of significance in the column. The required t-value is the value that intersects this row and column.

The critical value of t with 26 degrees of freedom is obtained as 1.706 from the table.

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Answer 2

Question

Chapter 9, Problem 1RE

(a)

To determine

The critical value of t at the confidence level of 99%.

(a)

Expert Solution

Answer to Problem 1RE

Solution: The critical value of t at 99% level of confidence for the sample size of n=18 is t0.005=2.898_.

Explanation of Solution

Given: The alpha is 0.01 and the size of the sample is n=18.

Explanation: For 99% confidence level, the confidence interval has 0.5% for its greater-than probability and 0.5% for its less-than probability. Hence, the required area is in the right tail of 0.005. Since the sample size is n=18, the degrees of freedom are 18−1=17.

Obtain the critical value of t by using the distribution table of the t-test. Then, look for 17 degrees of freedom in the row and 1% level of significance in the column. The required t-value is the value that intersects this row and column.

The critical value of t with 17 degrees of freedom is obtained as 2.898 from the table.

(b)

To determine

The critical value of t at 90% level of confidence.

(b)

Expert Solution

Answer to Problem 1RE

Solution: The critical value of t at 90% level of confidence for the sample size of n=27 is t0.05=1.706_.

Explanation of Solution

Given: The alpha is 0.1 and the size of the sample is n=27.

Explanation: For 90% confidence level, the confidence interval has 5% for its greater-than probability and 5% for its less-than probability. Hence, the required area is in the right tail of 0.05. Since the sample size is n=27, the degrees of freedom are 27−1=26.

Obtain the critical value of t by using the distribution table of the t-test. Then, look for 26 degrees of freedom in the row and 10% level of significance in the column. The required t-value is the value that intersects this row and column.

The critical value of t with 26 degrees of freedom is obtained as 1.706 from the table.

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Answer 3

Question

Chapter 9, Problem 1RE

(a)

To determine

The critical value of t at the confidence level of 99%.

(a)

Expert Solution

Answer to Problem 1RE

Solution: The critical value of t at 99% level of confidence for the sample size of n=18 is t0.005=2.898_.

Explanation of Solution

Given: The alpha is 0.01 and the size of the sample is n=18.

Explanation: For 99% confidence level, the confidence interval has 0.5% for its greater-than probability and 0.5% for its less-than probability. Hence, the required area is in the right tail of 0.005. Since the sample size is n=18, the degrees of freedom are 18−1=17.

Obtain the critical value of t by using the distribution table of the t-test. Then, look for 17 degrees of freedom in the row and 1% level of significance in the column. The required t-value is the value that intersects this row and column.

The critical value of t with 17 degrees of freedom is obtained as 2.898 from the table.

(b)

To determine

The critical value of t at 90% level of confidence.

(b)

Expert Solution

Answer to Problem 1RE

Solution: The critical value of t at 90% level of confidence for the sample size of n=27 is t0.05=1.706_.

Explanation of Solution

Given: The alpha is 0.1 and the size of the sample is n=27.

Explanation: For 90% confidence level, the confidence interval has 5% for its greater-than probability and 5% for its less-than probability. Hence, the required area is in the right tail of 0.05. Since the sample size is n=27, the degrees of freedom are 27−1=26.

Obtain the critical value of t by using the distribution table of the t-test. Then, look for 26 degrees of freedom in the row and 10% level of significance in the column. The required t-value is the value that intersects this row and column.

The critical value of t with 26 degrees of freedom is obtained as 1.706 from the table.

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Answer 4

Question

Chapter 9, Problem 1RE

(a)

To determine

The critical value of t at the confidence level of 99%.

(a)

Expert Solution

Answer to Problem 1RE

Solution: The critical value of t at 99% level of confidence for the sample size of n=18 is t0.005=2.898_.

Explanation of Solution

Given: The alpha is 0.01 and the size of the sample is n=18.

Explanation: For 99% confidence level, the confidence interval has 0.5% for its greater-than probability and 0.5% for its less-than probability. Hence, the required area is in the right tail of 0.005. Since the sample size is n=18, the degrees of freedom are 18−1=17.

Obtain the critical value of t by using the distribution table of the t-test. Then, look for 17 degrees of freedom in the row and 1% level of significance in the column. The required t-value is the value that intersects this row and column.

The critical value of t with 17 degrees of freedom is obtained as 2.898 from the table.

(b)

To determine

The critical value of t at 90% level of confidence.

(b)

Expert Solution

Answer to Problem 1RE

Solution: The critical value of t at 90% level of confidence for the sample size of n=27 is t0.05=1.706_.

Explanation of Solution

Given: The alpha is 0.1 and the size of the sample is n=27.

Explanation: For 90% confidence level, the confidence interval has 5% for its greater-than probability and 5% for its less-than probability. Hence, the required area is in the right tail of 0.05. Since the sample size is n=27, the degrees of freedom are 27−1=26.

Obtain the critical value of t by using the distribution table of the t-test. Then, look for 26 degrees of freedom in the row and 10% level of significance in the column. The required t-value is the value that intersects this row and column.

The critical value of t with 26 degrees of freedom is obtained as 1.706 from the table.

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Answer 5

Chapter 9, Problem 1RE

(a)

To determine

The critical value of t at the confidence level of 99%.

(a)

Expert Solution

Answer to Problem 1RE

Solution: The critical value of t at 99% level of confidence for the sample size of n=18 is t0.005=2.898_.

Explanation of Solution

Given: The alpha is 0.01 and the size of the sample is n=18.

Explanation: For 99% confidence level, the confidence interval has 0.5% for its greater-than probability and 0.5% for its less-than probability. Hence, the required area is in the right tail of 0.005. Since the sample size is n=18, the degrees of freedom are 18−1=17.

Obtain the critical value of t by using the distribution table of the t-test. Then, look for 17 degrees of freedom in the row and 1% level of significance in the column. The required t-value is the value that intersects this row and column.

The critical value of t with 17 degrees of freedom is obtained as 2.898 from the table.

(b)

To determine

The critical value of t at 90% level of confidence.

(b)

Expert Solution

Answer to Problem 1RE

Solution: The critical value of t at 90% level of confidence for the sample size of n=27 is t0.05=1.706_.

Explanation of Solution

Given: The alpha is 0.1 and the size of the sample is n=27.

Explanation: For 90% confidence level, the confidence interval has 5% for its greater-than probability and 5% for its less-than probability. Hence, the required area is in the right tail of 0.05. Since the sample size is n=27, the degrees of freedom are 27−1=26.

Obtain the critical value of t by using the distribution table of the t-test. Then, look for 26 degrees of freedom in the row and 10% level of significance in the column. The required t-value is the value that intersects this row and column.

The critical value of t with 26 degrees of freedom is obtained as 1.706 from the table.

Answer 6

Chapter 9, Problem 1RE

(a)

To determine

The critical value of t at the confidence level of 99%.

(a)

Expert Solution

Answer to Problem 1RE

Solution: The critical value of t at 99% level of confidence for the sample size of n=18 is t0.005=2.898_.

Explanation of Solution

Given: The alpha is 0.01 and the size of the sample is n=18.

Explanation: For 99% confidence level, the confidence interval has 0.5% for its greater-than probability and 0.5% for its less-than probability. Hence, the required area is in the right tail of 0.005. Since the sample size is n=18, the degrees of freedom are 18−1=17.

Obtain the critical value of t by using the distribution table of the t-test. Then, look for 17 degrees of freedom in the row and 1% level of significance in the column. The required t-value is the value that intersects this row and column.

The critical value of t with 17 degrees of freedom is obtained as 2.898 from the table.

Answer 7

Chapter 9, Problem 1RE

(a)

To determine

The critical value of t at the confidence level of 99%.

Answer 8

(a)

Expert Solution

Answer to Problem 1RE

Solution: The critical value of t at 99% level of confidence for the sample size of n=18 is t0.005=2.898_.

Answer 9

(a)

Expert Solution

Answer 10

(a)

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

Given: The alpha is 0.01 and the size of the sample is n=18.

Explanation: For 99% confidence level, the confidence interval has 0.5% for its greater-than probability and 0.5% for its less-than probability. Hence, the required area is in the right tail of 0.005. Since the sample size is n=18, the degrees of freedom are 18−1=17.

Obtain the critical value of t by using the distribution table of the t-test. Then, look for 17 degrees of freedom in the row and 1% level of significance in the column. The required t-value is the value that intersects this row and column.

The critical value of t with 17 degrees of freedom is obtained as 2.898 from the table.

Answer 13

(b)

To determine

The critical value of t at 90% level of confidence.

(b)

Expert Solution

Answer to Problem 1RE

Solution: The critical value of t at 90% level of confidence for the sample size of n=27 is t0.05=1.706_.

Explanation of Solution

Given: The alpha is 0.1 and the size of the sample is n=27.

Explanation: For 90% confidence level, the confidence interval has 5% for its greater-than probability and 5% for its less-than probability. Hence, the required area is in the right tail of 0.05. Since the sample size is n=27, the degrees of freedom are 27−1=26.

Obtain the critical value of t by using the distribution table of the t-test. Then, look for 26 degrees of freedom in the row and 10% level of significance in the column. The required t-value is the value that intersects this row and column.

The critical value of t with 26 degrees of freedom is obtained as 1.706 from the table.

Answer 14

(b)

To determine

The critical value of t at 90% level of confidence.

Answer 15

(b)

Expert Solution

Answer to Problem 1RE

Solution: The critical value of t at 90% level of confidence for the sample size of n=27 is t0.05=1.706_.

Answer 16

(b)

Expert Solution

Answer 17

(b)

Expert Solution

Answer 18

Expert Solution

Answer 19

Explanation of Solution

Given: The alpha is 0.1 and the size of the sample is n=27.

Explanation: For 90% confidence level, the confidence interval has 5% for its greater-than probability and 5% for its less-than probability. Hence, the required area is in the right tail of 0.05. Since the sample size is n=27, the degrees of freedom are 27−1=26.

Obtain the critical value of t by using the distribution table of the t-test. Then, look for 26 degrees of freedom in the row and 10% level of significance in the column. The required t-value is the value that intersects this row and column.

The critical value of t with 26 degrees of freedom is obtained as 1.706 from the table.