Chapter 9, Problem 1RE

(a)

To determine

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

Answer to Problem 1RE

Solution: The critical value of t at 99% level of confidence for the sample size of $n=18$ is $\underset{\_}{t_{0.005}=2.898}$.

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.

Answer to Problem 1RE

Solution: The critical value of t at 90% level of confidence for the sample size of $n=27$ is $\underset{\_}{t_{0.05}=1.706}$.

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.