A random sample of 16 students showed that the variance in t

A random sample of 16 students showed that the variance in the number of hours they spend studying for a final exam was 25 hours². Test, at the 5% level of significance, whether the population standard deviation of hours spent studying is less than 10. Use the critical value approach.

Solution

Let o be the standard deviation

The test hypothesis:

Ho: o=10 (i.e. null hypothesis)

Ha: o<10 (i.e. alternative hypothesis)

The test statistic is

chisquare= (n-1)*s^2/o^2

=(16-1)*25/10^2

=3.75

The degree of freedom =n-1=16-1=15

It is a left-tailed test.

Given a=0.05, the critical value of X^2 with 0.05 and df=15 is 7.26 (from chisquare table)

The rejection region is X^2<7.26, we reject the null hypothesis.

Since 3.75 is less than 7.26, we reject the null hypothesis.

So we can conclude that the population standard deviation of hours spent studying is less than 10.