Question

According to the Alaska Beer Institute (ABI) Annual Report for 2010, the mean annual beer consumption of beer per person in Anchorage, Alaska is 28.2 gallons (roughly 300 twelve ounce bottles). The City of Anchorage, Alcohol Review Board in 2018 wanted to put these results to the test and took a random sample of 27 Anchorage residents that yielded a sample mean of 23 gallon per person with a sample standard deviation of 6 gallon per person. Test the null hypothesis that there has been a significant decline in the beer consumption per person. Assume the population standard deviation is unknown. Use a t-test procedure. 04-1% , (12 pts)

Answer 1

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: ? = 28.2

Ha: ? < 28.2

This corresponds to a left-tailed test.

(2) Rejection Region

The significance level is ?=0.05, and the critical value for a left-tailed test is tc?=?1.706.

The rejection region for this left-tailed test is R = {t: t < -1.706}.

(3) Test Statistics

The t-statistic is computed as follows:

(4) Decision about the null hypothesis

Since it is observed that t=?4.503 < tc?=?1.706, it is then concluded that the null hypothesis is rejected.

Using the P-value approach: The p-value is p = 0.0001, and since p = 0.0001 < 0.05, it is concluded that the null hypothesis is rejected.

(5) Conclusion

There is enough evidence to claim that the population mean ? is less than 28.2, at the 0.05 significance level.