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. A random sample of 36 job applicants are selected from a large university, and they produce a sample mean score of 165 with a sample standard deviation of 12. At the 0.05 significance level, test the claim that the mean score for students from this university is greater than 160. State the null and alternative hypotheses symbolically. Which test procedure is appropriate to perform the required hypothesis test? Compute the value of the test statistic. Determine the P-value or provide the rejection region. What is your conclusion about the hypothesis test?

Answer 1

Since the computed value of t= 0.833 does not fall in the critical region we therefore do not reject H0 and may conclude that population mean is greater than 160. Or the sample comes from population with mean of 165.

Explanation:

1. State the null and alternative hypothesis as

H0: μ= 160 against the claim Ha :μ ≠160

Sample mean = x`= 165

Sample standard deviation= Sd= 12

2. The test statistic to use is

t= x`-μ/sd/√n

which if H0 is true , has t distribution with n-1 = 36-1= 35 degrees of freedom

3. The critical region is t< t (0.025(35)= 2.0306

t= x`-μ/sd/√n

4. t = (165-160)/[12/√(36)] = 5/[6] = 0.833

5. Since the computed value of t= 0.833 does not fall in the critical region we therefore do not reject H0 and may conclude that population mean is greater than 160. Or the sample comes from population with mean of 165.

Now

6. The p-value is 0 .410326 for t= 0.8333 with 35 degrees of freedom.