Question

The Dean of the College of Liberal Arts and Sciences (CLAS) reported that the mean time for CLAS students to complete their degree at CU-Denver is less than 5 years. She randomly selected a sample of 25 recent CLAS graduates and found that their mean time to graduate was 4.75 years with a sample standard deviation of 0.8 years. At an α = 0.1 level, is their sufficient evidence to conclude that the mean time for CLAS students to complete their degree is less than 5 years?

1. State the hypotheses and identify the claim. Use appropriate notation

2. Find the critical value(s) from the appropriate table. Include the appropriate drawing of the critical & non-critical region

3. Compute the test value and p-value. Include the appropriate formula

4. Make the decision to reject or not reject the null hypothesis

5. Summarize the results in the context of this problem

Answer 1

Ans:

n=25

df=25-1=24

critical t value=-1.318

Critical rejection region: t<-1.318

Test statistic:

t=(4.75-5)/(0.8/sqrt(25))

t=-1.5625

p-value=tdist(1.5625,24,1)=0.0656

As,p-value<0.1,we reject the null hypothesis.

There is sufficient evidence to support the claim that the mean time for CLAS students to complete their degree is less than 5 years.