1. The heights were recorded for a Simple Random Sample of 270 freshmen. The mean of this sample was 66.5 inches. The heights are known to be Normally Distributed with a population standard deviation of 5.1 inches. Round answers to one decimal place. (You do not need a data set for this problem.)
a. From the simple random sample of 270 freshmen heights:
i. Calculate the 96% Confidence Interval for the population mean height of a freshman. Interpret the confidence interval. Use MINITAB to compute the confidence interval. (Copy and paste the MINITAB output found in the Session window after your answer.)
ii. Calculate the 87% Confidence Interval for the population mean height of a freshman. Interpret the confidence interval. Use MINITAB to compute the confidence interval. (Copy and paste the MINITAB output found in the Session window after your answer.)
iii. As you increase the level of confidence, how will this affect the precision (i.e., the width) of the interval? (Note: The smaller the interval, the more precise it is.)
iv. What sample size would you need for a 95% Confidence Interval to have margin of error of no more than 0.45?
b. At a 0.05 significance level, test the claim that the average height of a freshman differs from the 1956 average freshman height of 65.7 inches.
i. State the null and alternative hypotheses.
ii. State the significance level for this problem.
iii. State the test statistic. Use MINITAB to compute the test statistic and P-value. (Copy and paste the MINITAB output found in the Session window after your answer. Use this result to answer part (iv)).
iv. State the P-value.
v. State whether you reject or do not reject the null hypothesis.
vi. State your conclusion in context of the problem.
vii. If the true mean was 65.7 inches, did you make an error? If so, which error? (Answer in complete sentences. You need to explain why or why not you made an error as well as identifying the type of error (Type I or II) if you did make an error. DO NOT answer these questions with a simple "Yes" or "No"; if you do, it will be marked as incorrect.)
2. Sulfur compounds cause "off-odors" in wine, so winemakers want to know the odor threshold, the lowest concentration of a compound that the human nose can detect. The odor threshold for dimethyl sulfide (DMS) in trained wine tasters is about 25 micrograms per liter of wine (µg/l).
The untrained noses of consumers may be less sensitive, however. Here are the DMS odor thresholds for 10 untrained students:
31 31 43 36 23 34 32 30 20 24
Assume that the odor threshold for untrained noses is Normally distributed with a population standard deviation of 6.7 g/l.
Type the above data in column 1 in MINITAB worksheet and answer the following questions.
Round answers to one decimal place.
a. Calculate the 94% confidence interval for the mean DMS odor threshold among all untrained students. Interpret the confidence interval. (Copy and paste the MINITAB output found in the Session window after your answer.)
b. How large a sample is needed so that the margin of error is within 1.6 µg/l for a 95% confidence level?
c. At a 0.05 significance level, test the claim that the mean threshold for untrained tasters is greater than 25.1µg/l.
i. State the null and alternative hypotheses.
ii. State the significance level for this problem.
iii. State the test statistic. Use MINITAB to compute the test statistic and P-value. (Copy and paste the MINITAB output found in the Session window after your answer. Also, use this result to answer part (iv)).
iv. State the P-value.
v. State whether you reject or do not reject the null hypothesis.
vi. State your conclusion in context of the problem.
vii. If the true mean was 30.8 µg/l, did you make an error? If so, which error? (Remember to answer in complete sentences. You need to explain why or why not you made an error as well as identifying the type of error (Type I or II) if you did make an error. DO NOT answer these questions with a simple "Yes" or "No"; if you do, it will be marked as incorrect.)