Question

A random sample of 8888 eighth grade​ students' scores on a national mathematics assessment test has a mean score of 278278. 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 270270. Assume that the population standard deviation is 3838. At alphaαequals=0.150.15​, is there enough evidence to support the​ administrator's claim? Complete parts​ (a) through

Answer 1

Since p <alpha, the administrator's declaration is correct.

Explanation:

Given that sample size n = 88, for eight 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

x bar >270

(One tailed test at 15% sign level)

Since sigma, population sd is known and sample size is large we use z test

Std error =

Mean difference 278-270=8

Z statistic = p value = 0.024

Since p <alpha, the administrator's declaration is correct.

Answer 2

Explanation:

Given that sample size n = 88, for eight 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

x bar >270

`H_0: xbar = 270\\H_a: x bar >270`

(One tailed test at 15% sign level)

Since sigma, population sd is known and sample size is large we use z test

Std error =
`(\sigma)/(√(n) ) =4.051`

Mean difference 278-270=8

Z statistic =
`(8)/(4.051) =1.975`

p value = 0.024

Since p <alpha, the administrator's declaration is correct.