Question

A random sample of 78 eighth grade students' scores on a national mathematics assessment test has a mean score of 276. 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 31. At a= 0.09, is there enough evidence to support the administrator's claim? Complete parts (a) through (e). (a) Write the claim mathematically and identify Ho and H. Choose the correct answer below. O A. Ho:<270 Ha:2 270 (claim) OD. Hops 270 Har> 270 (claim) O B. Ho: u = 270 (claim) Ha:> 270 O E. Ho: 5270 (claim) Ha::> 270 0 C. Ho: H = 270 Ha> 270 (claim) OF. Ho: H2 270 (claim) Hau<270 (b) Find the standardized test statistic z, and its corresponding area. z= (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. O O Reject Ho Fail to reject Ho

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 270
Alternative Hypothesis, Ha: μ > 270 (claim)
option D

Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (276 - 270)/(31/sqrt(78))
z = 1.71

P-value Approach
P-value = 0.044

As P-value < 0.09, reject the null hypothesis.

There is enough evidence to conclude the