Question

An article in the San Jose Mercury News stated that students in the California state university system take 4 years, on average, to finish their undergraduate degrees. A freshman student believes that the mean time is less and conducts a survey of 68 students. The student obtains a sample mean of 5.7 with a sample standard deviation of 0.6. 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% of all college students in the local area? Select one.
   • No
   • Yes
2. Is n≥30 ? Select one.
   • 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. Select one.
   • Fail to reject the null hypothesis.
   • Reject the null hypothesis.
5. Write the conclusion. Select one.
   • 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 4 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 4 years.

Answer 1