Question

An article in the San Jose Mercury News stated that students in the California state university system take 5 years, on average, to finish their undergraduate degrees. A freshman student believes that the mean time is less and conducts a survey of 38 students. The student obtains a sample mean of 4.4 with a sample standard deviation of 0.3. Is there sufficient evidence to support the student's claim at an α=0.01α=0.01 significance level?

1. Determine the test statistic. Round to four decimal places.
   t=t=
   
2. Find the pp-value. Round to 4 decimals.
   pp-value =

Answer 1

Solution :

This is the left tailed test,  

The null and alternative hypothesis is ,

H0 :   = 5

Ha : < 5

Test statistic = t =

= ( - ) / s / n

= (4.4 - 5) / 0.3 / 38

Test statistic = t = -12.3288

degrees of freedom = n - 1 = 38 - 1 = 37

P(t < -12.3288)

P-value = 0

= 0.01

P-value <

Reject the null hypothesis .