Questions: You wish to test the claim that the mean GPA of night students is larger than 2.6 at the .01 significance level. Based on a sample of 20 people, the sample mean GPA was 2.65 with a standard deviation of 0.08. When finding the critical value and test statistic, which distribution would we be using? - Normal distribution (invNorm for critical value) - T distribution (invT for critical value) - χ^2 distribution (inv χ for critical value) - F distribution (invF for critical value)

You wish to test the claim that the mean GPA of night students is larger than 2.6 at the .01 significance level. Based on a sample of 20 people, the sample mean GPA was 2.65 with a standard deviation of 0.08. When finding the critical value and test statistic, which distribution would we be using? - Normal distribution (invNorm for critical value) - T distribution (invT for critical value) - χ^2 distribution (inv χ for critical value) - F distribution (invF for critical value)
Transcript text: You wish to test the claim that the mean GPA of night students is larger than 2.6 at the .01 significance level. Based on a sample of 20 people, the sample mean GPA was 2.65 with a standard deviation of 0.08 . When finding the critical value and test statistic, which distribution would we be using? Normal distribution (invNorm for critical value) T distribution (invT for critical value) $\chi^{2}$ distribution (inv $\chi$ for critical value) F distribution (invF for critical value) Question Help: Message instructor Submit Question
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Solution

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Solution Steps

Step 1: Calculate the Standard Error

The standard error \( SE \) is calculated using the formula:

\[ SE = \frac{\sigma}{\sqrt{n}} = \frac{0.08}{\sqrt{20}} \approx 0.0179 \]

Step 2: Calculate the Test Statistic

The test statistic \( t_{\text{test}} \) is calculated using the formula:

\[ t_{\text{test}} = \frac{\bar{x} - \mu_0}{SE} = \frac{2.65 - 2.6}{0.0179} \approx 2.7951 \]

Step 3: Calculate the P-value

For a right-tailed test, the p-value is calculated as:

\[ P = 1 - T(z) \approx 0.0058 \]

Step 4: Determine the Distribution Used

Since the sample size is \( n = 20 \) and the population standard deviation is unknown, we use the t-distribution for this hypothesis test.

Final Answer

The test statistic is \( t \approx 2.7951 \), the p-value is \( 0.0058 \), and the distribution used is the T distribution.

Thus, the answer is:

\(\boxed{\text{T distribution (invT for critical value)}}\)

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