Question

Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Use either the traditional method or P-value method as indicated. Identify the null and alternative hypotheses, test statistic, critical value(s) or P-value (or range of P-values) as appropriate, and state the final conclusion that addresses the original claim.

Use a significance level of α = 0.01 to test the claim that μ > 2.85. The sample data consist of 9 scores for which   = 3.2 and s = 0.6. Use the traditional method of testing hypotheses

Answer 1

Solution :

The null and alternative hypothesis is ,

H0 :   = 2.85

Ha : > 2.85

Test statistic (t) =

= ( - ) / s / n

= (3.2 - 2.85) / 0.6 / 9

Test statistic = 1.75

P-value = 0.0653

= 0.01

P-value >

Fail to reject the null hypothesis .

There is insufficient evidence to support the claim.