A random sample of 76 eighth grade​ students' scores on a national mathematics assessment test has a mean score of 267. 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 260. 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).

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A random sample of 76 eighth grade​ students' scores on a national mathematics assessment test has a mean score of 267. 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 260.

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 random sample of 76 eighth grade students' scores on a national mathematics assessment test has a mean score of 267. 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 260. Assume that the population standard deviation is 33. At a = 0.11, is there enough evidence to support the
administrator's claim? Complete parts (a) through (e).
(a) Write the claim mathematically and identify Ho and Ha. Choose the correct answer below.
Ο Α. H: μ2 260 (claim)
O B. Ho: µ= 260 (claim)
Ha:µ > 260
O C. Ho: µs 260 (claim)
Ha: µ> 260
Ha:µ<260
O D. Ho: µ = 260
Ha: µ> 260 (claim)
O E. Ho: µs260
Ha: µ> 260 (claim)
O F. Ho: µ<260
Ha: µ2 260 (claim)
(b) Find the standardized test statistic z, and its corresponding area.
(Round to two decimal places as needed.)
(c) Find the P-value.
P-value =|(Round to three decimal places as needed.)
(d) Decide whether to reject or fail to reject the null hypothesis.
Reject Ho
Fail to reject Ho
(e) Interpret your decision in the context of the original claim.
At the 11% significance level, there
V enough evidence to
the administrator's claim that the mean score for the state's eighth graders on the exam is more than 260.
Transcribed Image Text:A random sample of 76 eighth grade students' scores on a national mathematics assessment test has a mean score of 267. 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 260. Assume that the population standard deviation is 33. At a = 0.11, is there enough evidence to support the administrator's claim? Complete parts (a) through (e). (a) Write the claim mathematically and identify Ho and Ha. Choose the correct answer below. Ο Α. H: μ2 260 (claim) O B. Ho: µ= 260 (claim) Ha:µ > 260 O C. Ho: µs 260 (claim) Ha: µ> 260 Ha:µ<260 O D. Ho: µ = 260 Ha: µ> 260 (claim) O E. Ho: µs260 Ha: µ> 260 (claim) O F. Ho: µ<260 Ha: µ2 260 (claim) (b) Find the standardized test statistic z, and its corresponding area. (Round to two decimal places as needed.) (c) Find the P-value. P-value =|(Round to three decimal places as needed.) (d) Decide whether to reject or fail to reject the null hypothesis. Reject Ho Fail to reject Ho (e) Interpret your decision in the context of the original claim. At the 11% significance level, there V enough evidence to the administrator's claim that the mean score for the state's eighth graders on the exam is more than 260.
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