Question

A local university claims that if you enroll in their university you will have your degree completed within 4.5 years. To test this a sample of 81 graduates was taken. The sample yielded an average of 4.75 years with a standard deviation of 1.2 years.

a. Set up the Hypothesis to test this University’s Claim at a level of significance of .05. (α=.05)

b. What is the Test Statistic and Critical Value for the above problem? What is the P-value for the above problem?

c. Would you reject the Null Hypothesis based on information obtained in part b.

Answer 1

Given that, smaple size ( n ) = 81

sample mean = 4.75 years

sample standard deviation ( s ) = 1.2 years

significance level = 0.05

a) The null and the alternative hypotheses are,

b) The test statistic is,

t = 1.875

since, it is two-tailed test, the critical values at with degreea of freedom = 81 - 1 = 80 are,

Critical values = -1.990, +1.990

p-value = 0.0644

c) Here, p-value = 0.0644 is greater than

so, we do not reject the null hypothesis ( H₀ ).