Questions 14, 15, 16: A large software company gives job applicants a test of pr

Question

Questions 14, 15, 16:

A large software company gives job applicants a test of programming ability. In the past, the mean for that test has been 160. 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.

14.) Using appropriate notation, identify the null hypothesis and alternative hypothesis..

15.) Give your minitab output, the p-value and your decision. State your conclusion.

16.) Calculate and interpret a 95% confidence interval for the average score on the test of programming ability.

Explanation / Answer

14)

Null Hypothesis:

H0: µ 160

Alternative Hypothesis:

H1: µ> 160

15)

One-Sample T

Test of mu = 160 vs > 160

                                  95%

                                Lower

N     Mean   StDev SE Mean    Bound     T      P

25 183.000 12.000    2.400 178.894 9.58 0.000

Here the p-value is .000 which is less .05 (level of significance); we reject the null hypothesis. There is sufficient evidence to conclude that the population mean score is greater than 160.

16)

Confidence Interval

X bar (-/+) E

X bar = 183

E = tc * SE = tc * 2.400

The critical value for 24 degrees of freedom at 5% level of significance is given as 2.064

E = 2.064*2.4 = 4.95

183 - 4.95 and 183 + 4.95

178.05 and 187.95

The 95% confidence interval is (178.05 and 187.95)

Here we are 95% confidence that the population mean will lie in between 178.05 and 187.95.

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