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. twenty-five job applicants are randomly selected from one large university and they produce a mean score and standard deviation of 183 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.

Answer 1

See attachment for answer.

Answer 2

Step-by-step explanation:

Mean of the test of programming ability was 160 in the past.

Again now, twenty-five job applicants are randomly selected from one university and they produce a mean score and standard deviation of 183 and 12.

So in this case, the null hypothesis will be,

$H_o: \mu = 160$

and alternate hypothesis will be,

$H_a: \mu > 160$

Mean of the sample = $\overline{x}$ = 183

Standard deviation of the sample = $\sigma$ = 12

sample size = n = 25

Using t distribution,

$t=\dfrac{\overline{x}-\mu}{\frac{\sigma}{\sqrt{n}}}$

$=\dfrac{183-160}{\frac{12}{\sqrt{25}}}$

$=9.58$

P-value =$P(t > 9.58)\approx 0$

As the obtained value is less than 0.05 or 5% level of significance, so we have to reject the null hypothesis.