Question

A random sample of 83 eighth grade​ students' scores on a national mathematics assessment test has a mean score of 278. This test result prompts a state school administrator to declare that the mean score for the​ state's eighth-graders on this test is more than 275. Assume that the population standard deviation is 35. At α=0.08 is there enough evidence to support the​ administration's claim? Complete parts​ (a) through​ (e).

A is done

B: fine the standardized test statistic z, and its corresponding area. Z= (round to two decimal points)

C: find the p-value

D: decide whether to reject or fail to reject the null hypothesis

Answer 1

Solution :-

Givan that ,

= 275

= 278

= 35

n = 83

This is the right  tailed test .

The null and alternative hypothesis is ,

H0 :   = 275

Ha : > 275

Test statistic = z

= ( - ) / / n

= ( 278 - 275) / 35 / 83

= 0.78

The test statistic = 0.78

P - value = P( Z > 0.78 )

= 1 - P ( Z < 0.78 )

= 1 - 0.7823

=0.2177

P-value = 0.2177

= 0.08

0.2177 > 0.08

P-value >  

Fail to reject the null hypothesis .

There is not sufficient evidence to claim