A company is willing to renew its advertising contract with a local radio station only if the station can show that at least 20% of residents of the city have heard the ad and recognize the company's product. The radio station conducts a random phone survey of 400 people.
(a) What would be the appropriate null hypothesis?
(b) What would be the appropriate alternative hypothesis?
(c) Is this a one or two-tailed test?
7. A nutrition lab is interested in the mean sodium content in a new "reduced sodium" hot dog. They sample 25 hot dogs and record a sample mean of 322 mg and a sample standard deviation of 14 mg.
(a) What would be the appropriate critical value to construct a 90% confidence interval?
(b) The 90% confidence interval for the mean sodium content of the hot dogs is found to be (317.2, 326.8). How would we interpret this confidence interval? (Pick one)
i. There is a 90% chance that the true mean sodium content is between 317.2 and 326.8 mg.
ii. There is a 90% probability that the true mean sodium content is between 317.2 and 326.8 mg.
iii. We are 90% confident that the true mean sodium content in the hotdogs is between 317.2 and 326.8 mg.
(c) Suppose we conducted a 90% confidence hypothesis test with the H0: μ = 325 and HA: μ ≠ 325. What would we conclude? Hint: You can use the confidence interval from (b) to help you decide.
8. Consumer Reports tested a sample of 11 brands of vanilla yogurt and found these number of calories per serving: 130, 160, 150, 120, 120, 110, 170, 160, 110, 130, 90. The sample mean is 131.82 and the sample standard deviation is 25.23. Suppose we wish to conduct a hypothesis test to determine whether the mean calorie content is less than 120 calories.
(a) What would be the appropriate test statistic? Enter your answer to two decimal places.
(b) Assuming the null hypothesis is true, what distribution will the test statistic follow? If it's appropriate, make sure to include the degrees of freedom.
9. In a report by the National Association of Colleges and Employers (NACE), the average starting salary for graduates in Accounting is $48,993.00. In a random sample of 50 graduates with degrees in Information Technology (IT), the mean starting salary was $52,089.00 with a standard deviation of $13,500.00. At the 0.01 significance level, test the claim that the mean starting salary for all IT graduates is greater than the reported mean starting salary for Accounting graduates.
Let μ represent the mean starting salary for all IT graduates. We test H0: μ = 48993 and HA: μ > 48993. We calculate the appropriate test statistic, which is 1.62, which follows a t-distribution with 49 degrees of freedom.
(a) What would be the appropriate p-value for this test? Report your answer to 4 decimal places.
(b) What would be the appropriate conclusion using α = 0.01?
(c) Would your conclusion change if we used α = 0.1 instead of α = 0.01?
10. Results of a poll evaluating support for drilling for oil and natural gas off the coast of California. Suppose the number of college grads and non-college grads was fixed prior to the study.
Support
Oppose or Do not Know Total
College Grad 164
236
400
Not College Grad 132
268
400
(a) What percent of college graduates and what percent of the non-college graduates in this sample support drilling for oil and natural gas off the Coast of California?
(b) Conduct a hypothesis test to determine if the data provide strong evidence that the proportion of college graduates who support off-shore drilling in California is different than that of non-college graduates. Be sure to clearly state the null and alternative hypotheses in symbols and in words, the test statistic you choose to use, its distribution, the p-value, and your conclusions. (Use α = 0.05)