The following information is available for two samples selected from independent normally distributed populations. Complete parts (a) and (b). Population A: n=13 s² = 63.2 S² = 17.5 Population B: n = 16 a. At the 0.05 level of significance, is there evidence of a difference between o? and o?? Determine the hypotheses. Choose the correct answer below. OA. Ho: oso H₂:0² > 0² C. H₂:0² = 0² H₂:0² +0² Use technology to find the test statistic, FSTAT FSTAT = C (Round to two decimal places as needed.) OB. Ho: 002 H₂:0² = 0² OD. Ho: 020² H₂:0² <0²

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The following information is available for two samples selected from independent normally distributed populations. Complete parts (a) and (b).

Population A:  
- \( n = 13 \)  
- \( S^2 = 63.2 \)

Population B:  
- \( n = 16 \)  
- \( S^2 = 17.5 \)

---

**a. At the 0.05 level of significance, is there evidence of a difference between \(\sigma^2_1\) and \(\sigma^2_2\)?**

Determine the hypotheses. Choose the correct answer below.

- \( \circ \) A. \( H_0: \sigma^2_1 \leq \sigma^2_2 \)  
   \( H_1: \sigma^2_1 > \sigma^2_2 \)

- \( \circ \) B. \( H_0: \sigma^2_1 \neq \sigma^2_2 \)  
   \( H_1: \sigma^2_1 = \sigma^2_2 \)

- \( \checkmark \) C. \( H_0: \sigma^2_1 = \sigma^2_2 \)  
   \( H_1: \sigma^2_1 \neq \sigma^2_2 \)

- \( \circ \) D. \( H_0: \sigma^2_1 = \sigma^2_2 \)  
   \( H_1: \sigma^2_1 < \sigma^2_2 \)

Use technology to find the test statistic, \( F_{\text{STAT}} \):

\( F_{\text{STAT}} = \underline{\quad} \) (Round to two decimal places as needed.)
Transcribed Image Text:The following information is available for two samples selected from independent normally distributed populations. Complete parts (a) and (b). Population A: - \( n = 13 \) - \( S^2 = 63.2 \) Population B: - \( n = 16 \) - \( S^2 = 17.5 \) --- **a. At the 0.05 level of significance, is there evidence of a difference between \(\sigma^2_1\) and \(\sigma^2_2\)?** Determine the hypotheses. Choose the correct answer below. - \( \circ \) A. \( H_0: \sigma^2_1 \leq \sigma^2_2 \) \( H_1: \sigma^2_1 > \sigma^2_2 \) - \( \circ \) B. \( H_0: \sigma^2_1 \neq \sigma^2_2 \) \( H_1: \sigma^2_1 = \sigma^2_2 \) - \( \checkmark \) C. \( H_0: \sigma^2_1 = \sigma^2_2 \) \( H_1: \sigma^2_1 \neq \sigma^2_2 \) - \( \circ \) D. \( H_0: \sigma^2_1 = \sigma^2_2 \) \( H_1: \sigma^2_1 < \sigma^2_2 \) Use technology to find the test statistic, \( F_{\text{STAT}} \): \( F_{\text{STAT}} = \underline{\quad} \) (Round to two decimal places as needed.)
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