Question

13) A large software company gives job applicants a test of programming ability, and the mean for the test has been 160 in the past. Twenty-five applicants are randomly selected from one large university and they produce a mean score of 165, with a standard deviation of 13. Conduct a t-test at a significance level of 0.05 to see if we have evidence to indicate that the sample comes from a population with a mean score that differs from 160?

Answer 1

Define the null and the alternative hypothesis as

Ho :μ = 160 H, :μέ 160

The test is two tailed test and sample size is 25, with sample mean 165 and sample standard deviation as 13

So the value of the test static is

$t={\bar{x}-\mu \over s/\sqrt{n}}={165-160\over 13/\sqrt{25}}={25\over 13}\approx 1.92$

As the test significance level is 0.05, and test is two tailed with number of degrees of freedom $n-1=25-1=24$

So, P-value is $\Pr(|t| >| 1.92|)=0.0668$

As 0.0668>0.05

So we fail to reject the null hypothesis

So there is not enough evidence to support the claim