1. Echinacea Treatment In a study designed to test the effectiveness of echinacea for treating upper respiratory tract infections in children, 337 children were treated with echinaceaand 370 other children were given a placebo. The numbers of days of peak severity ofsymptoms for the echinacea treatment group had a mean of 6.0 days and a standard deviation of2.3 days. The numbers of days of peak severity of symptoms for the placebo group had amean of 6.1 days and a standard deviation of 2.4 days

• Construct the 95% confidence interval for the mean number of days of peak severity of symptoms for those who receive echinacea treatment.
• Construct the 95% confidence interval for the mean number of days of peak severity of symptoms for those who are given a placebo.
• Compare the two confidence intervals. What do the results suggest about the effectiveness of echinacea?

2. Monitoring Lead in Air Listed below are measured amounts of lead (in micrograms percubic meter, or ) in the air. The Environmental Protection Agency (EPA) has established an air quality standard for lead . The measurements shown below wererecorded at Building 5 of the World Trade Center site on different days immediately followingthe destruction caused by the terrorist attacks of September 11, 2001. After the collapse of thetwo World Trade Center buildings, there was considerable concern about the quality of theair.

• Use the given values to construct a 95% confidence interval estimate of the mean amountof lead in the air. Is there anything about this data set suggesting that the confidence intervalmight not be very good? Explain.
• DATA:5.40, 1.10, 0.42, 0.73, 0.48, 1.10

3. Analysis of Pennies In an analysis investigating the usefulness of pennies, the cents portions of 100 randomly selected credit card charges are recorded. The sample has a mean of 47.6 cents and a standard deviation of 33.5 cents. If the amounts from 0 cents to 99 cents areall equally likely, the mean is expected to be 49.5 cents.

• Use a 0.01 significance level to test theclaim that the sample is from a population with a mean equal to 49.5 cents.
• What does the resultsuggest about the cents portions of credit card charges?

4. Analysis of Pennies In an analysis investigating the usefulness of pennies, the centsportions of 100 randomly selected checks are recorded. The sample has a mean of 23.8 centsand a standard deviation of 32.0 cents. If the amounts from 0 cents to 99 cents are all equallylikely, the mean is expected to be 49.5 cents.

• Use a 0.01 significance level to test the claim thatthe sample is from a population with a mean less than 49.5 cents.
• What does the result suggestabout the cents portions of the checks?