Question

A random sample of 78 eighth grade​ students' scores on a national mathematics assessment test has a mean score of 284.

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 275.

Assume that the population standard deviation is 32. At α=0.04​, is there enough evidence to support the​ administrator's claim.a)
H0​:μ≤275Ha​:μ>275​(claim)

b) find the standarized test statistic z and its corresponding areac) find the p valued) describe whether to reject or fail the null hypothesise) interpret your decision in the context of the original claim

Answer 1

a) In the step-by-step-explanation

b) z(s) = -2.46 corresponding area is 0.0069

P [ μ₀ > 275 ] is 0.0069 or 0.69 %

We reject H₀

Explanation:

Normal distribution

Random sample

size sample 78 = n

population standard deviation σ = 32

The school administrator declare that mean score is more (bigger than)

275. So the hypothesis test should be:

H₀ null hypothesis μ₀ > 275 and

Hₐ alternative hypothesis μ₀ < 275

Is one tail test with α = 0,04 from tables we have z(c) = - 176

We proceed to compute z(s)

z(s) = [ (μ - μ₀) /( σ /√n) ] ⇒ z(s) = (- 9 *√78 )/ 32

z(s) = - (9*8.83)/32

z(s) = - 2.46 corresponding area is 0,0069

P [ z > 275 ] = 0.0069 or 0.69 %

The value for z(s) = - 2.46 is smaller than the critical value mentioned in problem statement z(c) = - 1.74 , the z(s) is in the rejection zone

Therefore we reject H₀