Question

An article in the San Jose Mercury News stated that students in the California state university system take 5.5 years, on average, to finish their undergraduate degrees. A freshman student believes that the mean time is less and conducts a survey of 60 students. The student obtains a sample mean of 4.9 with a sample standard deviation of 0.3. Is there sufficient evidence to support the student's claim at an α=0.1 significance level?

Preliminary:

1. Is it safe to assume that n≤5% of all college students in the local area?
   • No
   • Yes
   
   
2. Is n≥30?
   • Yes
   • No

Test the claim:

1. Determine the null and alternative hypotheses. Enter correct symbol and value.
   
   H0: μ=
   Ha: μ? < != >  
   
2. Determine the test statistic. Round to four decimal places.
   t=
   
3. Find the pp-value. Round to 4 decimals.
   p-value =
4. Make a decision.
   • Reject the null hypothesis.
   • Fail to reject the null hypothesis.
   
   
5. Write the conclusion.
   • There is sufficient evidence to support the claim that the mean time to complete an undergraduate degree in the California state university system is less than 5.5 years.
   • There is not sufficient evidence to support the claim that that the mean time to complete an undergraduate degree in the California state university system is less than 5.5 years.

Answer 1