Question

A large software company gives job applicants a test of programming ability and the mean for that test has been 160 in the past. Assume that the test scores are normally distributed. Twenty-five job applicants are randomly selected from one large university and they produce a mean score and standard deviation of 168 and 12, respectively. Use a 0.05 level of significance to test the claim that this sample comes from a population with a mean score greater than 160.

(a) Identify the null and alternative hypotheses

. (b) Find the test statistic.

(c) Calculate the P-value.

(d) Make conclusion about the null hypothesis and give the final conclusion that addresses the original claim.

Answer 1

Solution :

Given that ,

= 160

= 168

= 12

n = 25

The null and alternative hypothesis is ,

H₀ :   = 160

H_a : > 160

This is the right tailed test .

Test statistic = z

= ( - ) / / n

= ( 168 - 160) / 12 / 25

= 3.33

The test statistic = 3.33

P - value = P(Z > 3.33 ) = 1 - P (Z < 3.33 )

= 1 - 0.9996

= 0.0004

The P-value = 0.0004

= 0.05  

0.0004 < 0.05

P-value <

Reject the null hypothesis .

Final conclusion : - Reject Ho . There is sufficient evidence to test the claim that this sample comes from a population with a mean score greater than 160. at a 0.05 level of significance .