Question

Researchers collected a simple random sample of the times that 80 college students required to earn their bachelor’s degrees. The sample has a mean of 4.8 years and a standard deviation of 1.2 years. Use a 10% significance level to test the claim that the mean time for all college students is less than 5 years.

Answer 1

The hypotheses are :

H0 : The mean time for all college students is equal to 5 years , i.e , =5

H1 : The mean time for all college students is less than 5 years , i.e , <5

Here, n = 80 , = 4.8 and s = 1.2

alpha = 0.1

The test statistic , t = ( - ) / (s / n)\

= -0.2 / 0.134

= -1.493

Degrees of freedom = n -1

= 79

Now, at alpha = 0.1 and df = 79 , we find the critical value of t from the critical values table.

t(critical) = 1.292

Therefore , | t | > t(critical) and hence, we reject the null hypothesis at alpha = 0.1.

We conclude that the mean time for all college students is less than 5 years.