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 a large university and they produce a mean score of 183 and a standard deviation of 12. Use a 5% significance level and the critical-value method to test whether the mean score for students from this university is greater than 160. Assume the population is normally distributed. Correctly state a) your conclusion about what to do with H₀ AND b) your conclusion about the claim that is being made.

Answer 1

a)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 160
Alternative Hypothesis, Ha: μ > 160

Rejection Region
This is right tailed test, for α = 0.05 and df = 24
Critical value of t is 1.711.
Hence reject H0 if t > 1.711

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (183 - 160)/(12/sqrt(25))
t = 9.583

reject the null hypothesis.

b)

There is sufficient evidence to conclude that the mean score for students from this university is greater than 160