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 54 students. The student obtains a sample mean of 4.7 with a sample standard deviation of 1.2. 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?
   • Yes
   • No
   
   
2. Is n≥30n≥30 ?
   • Yes
   • No

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.

Answer 1

No, it is not safe to assume that n≤5%n≤5% of all college students in the local area.

Yes, it is correct n≥30n≥30 .

The null and alternative hypothesis :

Values ----> mean = 5.5 , n= 54 , x= 4.7 , s= 1.2 , alpha = 0.01 , df=(n-1) = 53

Calculating test-statistic :

test-statistic = -4.8990

P-value = 0.0000 (using t table with t= -4.8990 for a one tailed test)

[0.0000<0.01]

Decision : Reject the null hypothesis because p value is less than alpha .

Conclusion:  Yes, there is sufficient evidence to support the student's claim at an α=0.01 significance level that mean time is less than 5.5.