Question

An article in the San Jose Mercury News stated that students in the California state university...

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 =

Homework Answers

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 .

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