Question

1. Consider the following hypothesis test: Ho: μ = 15 H1: μ ≠ 15

A sample of 50 provided a sample mean of 15.15. The population standard deviation is 3.

a. Compute the value of the test statistic. b. What is the p value? c. At α = 0.05, what is the rejection rule using the critical value? What is your conclusion?

Answer 1

Solution:

This is a two tailed test.

a)

The test statistics,

Z =( - )/ (/n)

= ( 15.15 - 15 ) / ( 3 / 50 )

= 0.35

b)

P-value = 2 * P(Z > z )

= 2 * ( 1 - P(Z < 0.35 ))

= 2 * 0.3632

= 0.7264

c)

Critical value of  the significance level is α = 0.05, and the critical value for a two-tailed test is

= 1.96

The rejection region is,

Reject H0. if |z| > 1.96

Since it is observed that ∣z∣ = 0.35 < = 1.96, it is then concluded that the null hypothesis is not rejected.