Question

A home insurance company claimed that, because of the Covid-19 pandemic, resulting in less home invasions, they have reduced the monthly premiums that they charged per home by at least $50 per month on average. To test this claim, a random sample of 22 home policies were allowed to be looked at. This random sample compared the monthly premiums in June, 2020, with the monthly payment before the pandemic (February, 2020) and it was calculated that the monthly premium in June dropped by an average of $44 and that the standard deviation in this this drop in premiums was calculated to be $12.00. At the .05 level of significance, is there sufficient evidence that the insurance company’s claim is false? In answering this question, complete the following in the spaces provided (including diagrams):

Hypotheses

Test statistic

Decision rule

p-value

Conclusion

Answer 1

The null and alternate hypothesis are:

H0:

Ha:

The test statistic is given by:

Decision rule: We reject H0 if p-value is less than .

Since this is a left-tailed test, so the p-value is given by:

Since p-value is less than 0.05, so we have sufficient evidence to reject the null hypothesis H0.

Thus we can conclude that the company has reduced the monthly premiums that they charged per home by less than $50 per month on average.