graders on this exam is more than 270. Assume that the population standard deviation is 33. At a=0.11, is there enough evidence OE H, u2 270 (claim) OD. Ho H<270 H, u2 270 (claim) H, u<270 (b) Find the standardized test statistic z, and its corresponding area. z= 1.34 (Round to two decimal places as needed.) (c) Find the P-value. P-value = 0.0901 (Round to three decimal places as needed.) %3D (d) Decide whether to reject or fail to reject the null hypothesis. O Reject Ho Fail to reject Ho

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A random sample of 78 eighth-grade students' scores on a national mathematics assessment test has a mean score of 275. This test result prompts a state school administrator to declare that the mean score for the state's eighth graders on this exam is more than 270. Assume that the population standard deviation is 33. At α = 0.11, is there enough evidence to support the administrator's claim? Complete parts (a) through (e).

(a) Choose the correct hypotheses:
- \( H_0: \mu \leq 270 \) (claim)
- \( H_a: \mu > 270 \)

(b) Find the standardized test statistic z, and its corresponding area.
- \( z = 1.34 \) (Round to two decimal places as needed.)

(c) Find the P-value.
- P-value = 0.0901 (Round to three decimal places as needed.)

(d) Decide whether to reject or fail to reject the null hypothesis.
- Fail to reject \( H_0 \)

(e) [This part is not visible in the image.]

Explanation: 
This text is part of a hypothesis testing problem where the claim in question is whether the mean score for the state's eighth graders exceeds 270. The hypothesis test uses the z-statistic calculated to compare against a significance level (\( \alpha = 0.11 \)). The resulting P-value helps determine if there is sufficient evidence to support the claim, leading to a failure to reject the null hypothesis in this scenario.
Transcribed Image Text:A random sample of 78 eighth-grade students' scores on a national mathematics assessment test has a mean score of 275. This test result prompts a state school administrator to declare that the mean score for the state's eighth graders on this exam is more than 270. Assume that the population standard deviation is 33. At α = 0.11, is there enough evidence to support the administrator's claim? Complete parts (a) through (e). (a) Choose the correct hypotheses: - \( H_0: \mu \leq 270 \) (claim) - \( H_a: \mu > 270 \) (b) Find the standardized test statistic z, and its corresponding area. - \( z = 1.34 \) (Round to two decimal places as needed.) (c) Find the P-value. - P-value = 0.0901 (Round to three decimal places as needed.) (d) Decide whether to reject or fail to reject the null hypothesis. - Fail to reject \( H_0 \) (e) [This part is not visible in the image.] Explanation: This text is part of a hypothesis testing problem where the claim in question is whether the mean score for the state's eighth graders exceeds 270. The hypothesis test uses the z-statistic calculated to compare against a significance level (\( \alpha = 0.11 \)). The resulting P-value helps determine if there is sufficient evidence to support the claim, leading to a failure to reject the null hypothesis in this scenario.
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