Question

A random sample of 81 eighth grade students' scores on a national mathematics assessment test has a mean score of 288. 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 280. Assume that the population standard deviation is 34. At alpha=0.06, is there enough evidence to support the administrator's claim?

(a) Write the claim mathematically and identify Upper H 0and Upper H Subscript a

(b) Find the standardized test statistic z, and its corresponding area

(c) Find the P-value.

(d) Decide whether to reject or fail to reject the null hypothesis.

Answer 1

a)

H0: <= 280

Ha: > 280 (Right tailed)

b)

Test statistics

z = - / ( / sqrt(n) )

= 288 - 280 / (34 / sqrt(81))

= 2.12

Critical value at 0.06 level is 1.5548

Rejection region - Reject H0 if test statistics > 1.5548

c)

p-value = P( Z > z)

= P( Z > 2.12)

= 0.017

d)

Since p-value < 0.06 level, we have sufficient evidence to reject null hypothesis.

We conclude at level that we have enough evidence to support the claim.