Question

An article in the San Jose Mercury News stated that students in the California state university system take 6 years, on average, to finish their undergraduate degrees. A freshman student believes that the mean time is less and conducts a survey of 39 students. The student obtains a sample mean of 5.7 with a sample standard deviation of 1.8. Is there sufficient evidence to support the student's claim at an α=0.01α=0.01 significance level?

Preliminary:

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

Test the claim:

1. Determine the null and alternative hypotheses. Enter correct symbol and value.
   
   H0H0: μ=μ=
   HaHa: μμ? != < >   
   
2. Determine the test statistic. Round to four decimal places.
   t=t=
   
3. Find the pp-value. Round to 4 decimals.
   pp-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 6 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 6 years.

Answer 1

it safe to assume that n≤5% of all college students in the local area

Yes

n≥30 ?

Yes

1. 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 6 years