Question

A general achievement test is standardized so that eighth graders should average 77.2 with a standard deviation of 4.8. If 35 eighth graders from a certain school district average 79.5 on the test, does this substantiate the claim that the eighth graders in this district are above average? Use the level of significance alpha = 0.05 and assume that the data constitute a random sample. State the hypotheses and conclusion.

Answer 1

H0: = 77.2

Ha: > 77.2

Test Statistic :-

Z = ( X - µ ) / ( σ / √(n))

Z = ( 79.5 - 77.2) / ( 4.8 / √( 35 ))

Z = 2.83

Test Criteria :-

Reject null hypothesis if Z > Z(α)

Critical value Z(α) = Z(0.05) = 1.645

Z < Z(α) = 2.83 < 1.645

Result :- Reject null hypothesis

Conclusion = We have sufficient evidence to conclude that the eighth graders in this district

are above average