1. ) Industry Research polled teenagers on sunscreen use. The survey revealed from a sample of 50 teenage girls 46% regularly used sunscreen before going out in the sun. The survey also revealed from a sample of 40 teenage boys 30% regularly used sunscreen before going out in the sun. Find a 90% confidence interval for the difference in the proportions of teenage girls and teenage boys who regularly use sunscreen before going out in the sun. ( 9 points )

2. ) A nurse claims that the variations of the lengths of newborn males is different

from the variations of the lengths of newborn females. A sample of 15 newborn males is selected, and the standard deviation is 1.3 inches. The standard deviation of a sample of 15 newborn females is 0.9 inches. Assuming that the lengths from each population follow a normal distribution and using a=0.05, can the nurse conclude that the variation of lengths is different? ( 18 points )

3. ) The Rolling Stones, a rock group formed in the 1960s, has toured extensively in

support of new albums. Pollstar has collected data on the earnings form the Stones’s North American tours. For 30 randomly selected Rolling Stones concerts, the mean gross earnings were $2.27 million with a standard deviation of $0.5 million. Obtain a 95% confidence interval for the mean gross earnings of all Rolling Stones concerts. ( 8 points )

4. ) The mean cost to community hospitals per patient per day in all U.S. hospitals was $1033 in 1997. In that same year, a random sample of 30 daily costs in Ohio hospitals had a mean of $1123. Assuming a population standard deviation of $350 for Ohio hospitals, do the data provide sufficient evidence to conclude that, in 1997, the mean cost in Ohio hospitals is different than the national mean? Perform the required hypothesis test at significance level. (18 points)

5. ) For each of the following problems the hypotheses for a particular test are stated

along with some critical information about the test. Use and this information to obtain the following for each test. ( 5 points each, 15 points total )

(I) Find the appropriate P-value for each test.

(II) Then state your statistical decision (Reject H_o or Fail to Reject H_o)

(a) H_o: m = 5 vs. H_a: m > 5 P-value = ____________________

n = 23 s = 4

Sample obtained from a Normal Distribution

Test Statistic = 1.23 Decision ____________________

(b) H_o: m = 10 vs. H_a: m ¹ 10 P-value = ____________________

n = 11 s = 2

Sample obtained from a Normal Distribution

Test Statistic = -1.80 Decision ____________________

(c) H_o: p = 0.10 vs. H_a: p < 0.10 P-value = ____________________

n = 100

Test Statistic = 2.00 Decision ____________________

6. ) A study by researchers at the University of Maryland addressed the question of

whether the mean body temperature of humans is 98.6°. Among other data, the researchers obtained the body temperatures of some 100 healthy humans and then used the data to test the following hypotheses. ( 3 points each, 12 points total )

H_o: m = 98.6° vs. H_a: m ¹ 98.6°. The four possible outcomes that could result are stated below. After each statement provide the appropriate description of the outcome (Type I error, Type II error, or Correct Decision).

_____________a. ) We conclude from the test that the mean body temperature of

humans is not 98.6°, when in fact the mean body temperature of humans is not 98.6°.

_____________b. ) We conclude from the test that the mean body temperature of humans is 98.6°, when in fact the mean body temperature of humans is not 98.6°.

_____________c. ) We conclude from the test that the mean body temperature of humans is not 98.6°, when in fact the mean body temperature of humans is 98.6°.

_____________d. ) We conclude from the test that the mean body temperature of humans is 98.6°, when in fact the mean body temperature of humans is 98.6°.

7. ) Glaucoma is a leading cause of blindness in the United States. N. Ehlers measured the corneal thickness of eight patients who had glaucoma in one eye but not in the other. The following are the data on corneal thickness, in microns.

Patient	1	2	3	4	5	6	7	8
Normal	484	478	492	444	436	398	464	476
Glaucoma	488	478	480	426	440	410	458	460

Do the data provide sufficient evidence to conclude that the mean corneal thickness is greater in normal eyes than in eyes with glaucoma? Use the classical approach and a 0.10 significance level. ( 20 points )