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.At a significance level of 0.05,does this indicate that the sample comes from a population with a mean score greater than 160?

Question

Quizplus · Accepted Answer

We need to conduct a one-sample t-test with the null hypothesis H0: μ = 160 (population mean score is 160) and the alternative hypothesis Ha: μ > 160 (population mean score is greater than 160). 
The test statistic is given by t = (x̄ - μ) / (s / √n) 
where x̄ = 165 is the sample mean, μ = 160 is the hypothesized population mean, s = 13 is the sample standard deviation, and n = 25 is the sample size. 
Plugging in the values, we get t = (165 - 160) / (13 / √25) = 1.92 
The degrees of freedom for the t-distribution is df = n - 1 = 24. 
Using a t-table or calculator, with α = 0.05 and df = 24, we find the critical value to be 1.711. 
The P-value is calculated as the probability of obtaining a t-statistic equal to or more extreme than 1.92 (in the right tail), which is P(T ≥ 1.92) = 0.0332. 
Since the P-value (0.0332) is less than the significance level (0.05), we reject the null hypothesis. 
Therefore, we have sufficient evidence to conclude that the population mean score is greater than 160. 
Thus, the correct answer is D.

A Large Software Company Gives Job Applicants a Test of Programming