Data from 1960 shows that the standard deviation of daily hi

Data from 1960 shows that the standard deviation of daily high temperatures in Villopolis was 5.6

Solution

Let o be the population standard deviation.

The test hypothesis:

Ho: o=7.6 (i.e. null hypothesis)

Ha: o>7.6 (i.e. alternative hypothesis)

The test statistic is

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

=(20-1)*5.6^2/7.6^2

=10.32

The degree of freedom =n-1=20-1=19

It is a right-tailed test.

Given a=0.05, the critical value of chisquare with 0.95 and df=19 is 30.14 (from chisquare table)

The rejection region is if X^2 >30.14, we reject the null hypothesis.

Since 10.32 is less than 30.14, we do not reject the null hypothesis.

Answer: There is not enough evidence to support the claim that the standard deviation has increased.