Questions: Homework Question 15, 7.2.5-T HW Score: 52%, 13 of 25 points Points: 0 of 1 Save Assume that we want to construct a confidence interval. Do one of the following, as appropriate: (a) find the critical value tα / 2, (b) find the critical value zα / 2, or (c) state that neither the normal distribution nor the t distribution applies. The confidence level is 99%, σ is not known, and the normal quantile plot of the 17 salaries (in thousands of dollars) of basketball players on a team is as shown. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. tα / 2= (Round to two decimal places as needed.) B. zα / 2= (Round to two decimal places as needed.) C. Neither the normal distribution nor the t distribution applies. Clear all Check answer Get more help

Homework Question 15, 7.2.5-T HW Score: 52%, 13 of 25 points Points: 0 of 1 Save Assume that we want to construct a confidence interval. Do one of the following, as appropriate: (a) find the critical value tα / 2, (b) find the critical value zα / 2, or (c) state that neither the normal distribution nor the t distribution applies. The confidence level is 99%, σ is not known, and the normal quantile plot of the 17 salaries (in thousands of dollars) of basketball players on a team is as shown. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. tα / 2= (Round to two decimal places as needed.) B. zα / 2= (Round to two decimal places as needed.) C. Neither the normal distribution nor the t distribution applies. Clear all Check answer Get more help
Transcript text: 7 Homework Question 15, 7.2.5-T HW Score: $52 \%, 13$ of 25 points Points: 0 of 1 Save Assume that we want to construct a confidence interval. Do one of the following, as appropriate: (a) find the critical value $t_{\alpha / 2}$, (b) find the critical value $z_{\alpha / 2}$, or (c) state that neither the normal distribution nor the $t$ distribution applies. The confidence level is $99 \%, \sigma$ is not known, and the normal quantile plot of the 17 salaries (in thousands of dollars) of basketball players on a team is as shown. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. $t_{\alpha / 2}=$ $\square$ (Round to two decimal places as needed.) B. $z_{\alpha / 2}=$ $\square$ (Round to two decimal places as needed.) C. Neither the normal distribution nor the $t$ distribution applies. Clear all Check answer Get more help -
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Solution

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Solution Steps

Step 1: Determine the Distribution to Use

Since the confidence level is 99% and the population standard deviation is not known, we need to use the t-distribution. The sample size is 17, which is less than 30, further confirming the use of the t-distribution.

Step 2: Find the Degrees of Freedom

The degrees of freedom (df) for the t-distribution is calculated as the sample size minus one. \[ df = n - 1 = 17 - 1 = 16 \]

Step 3: Find the Critical Value \( t_{\alpha/2} \)

Using a t-distribution table or calculator for a 99% confidence level and 16 degrees of freedom, we find the critical value \( t_{\alpha/2} \).

For a 99% confidence level: \[ \alpha = 1 - 0.99 = 0.01 \] \[ \alpha/2 = 0.01/2 = 0.005 \]

Looking up the value in the t-distribution table for 16 degrees of freedom and \( \alpha/2 = 0.005 \), we get: \[ t_{\alpha/2} \approx 2.921 \]

Final Answer

A. \( t_{\alpha/2} = 2.92 \) (Rounded to two decimal places)

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