Question

Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Use either the traditional method or P-value method as indicated. Identify the null and alternative hypotheses, test statistic, critical value(s) or P-value (or range of P-values) as appropriate, and state the final conclusion that addresses the original claim. 21) A large software company gives job applicants a test of programming ability and the mean 21) 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. Use the P-value method of testing hypotheses.

Answer 1

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

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

P-value Approach
P-value = 0
As P-value < 0.05, reject the null hypothesis.

Conclusion
There is sufficient evidence to conclude that sample comes from a population with mean score greater tahn 160