Question

Write the word or phrase that best completes each statement or answers the 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.
1) 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 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

Let be the true mean score of a test of programming ability for large university students.

Null Hypothesis H0: = 160

Altenative Hypothesis Ha: > 160

Sample mean, = 183

Sample standard deviation s = 12

Since we do not know the true population standard deviation we will conduct one sample t test.

Standard error of mean, SE = s / = 12 /  = 2.4

Test statistic, t = ( - ) / SE =  (183 - 160) / 2.4 = 9.58

Degree of freedom = n-1 = 25-1 = 24

For two-tail test, p-value = 2 * p(t > 9.58, df = 24) =  0.0000

Since, p-value is less than 0.05 significance level, we reject null hypothesis H0 and conclude that there is significant evidence that mean score of a test of programming ability for large university students is greater than 160.