1) In a sample of n=11 lichen specimens, the researchers found the mean and standard deviation of the amount of the radioactive element, cesium-137, that was present to be 0.009 and 0.005 microcurie per milliliter, respectively. Suppose the researchers want to increase the sample size in order to estimate the mean to within 0.001 microcurie per milliliter of its true value, using a 95% confidence interval. h

c. Compute the sample size necessary to obtain the desired estimate.

the sample size is (solve)

2) Health care workers who use latex gloves with glove powder on a daily basis are particularly susceptible to developing a latex allergy. Each in a sample of

47 hospital employees who were diagnosed with a latex allergy based on a skin-prick test reported on their exposure to latex gloves. Summary statistics for the number of latex gloves used per week are x=19.1

and s=11.9.

Complete parts

(a)(d).

Part 1

a. Give a point estimate for the average number of latex gloves used per week by all health care workers with a latex allergy.

enter your response here

Part 2

b. Form a 95% confidence interval for the average number of latex gloves used per week by all health care workers with a latex allergy.

enter your response here,enter your response here

3) A group of researchers wants to estimate the true mean skidding distance along a new road in a certain forest. The skidding distances (in meters) were measured at 20 randomly selected road sites. These values are given in the accompanying table. Complete parts a through d.

486	351	456	200	290	410	575	437	547	380
295	434	184	260	275	402	315	314	143	425

a.

Estimate the true mean skidding distance for the road with a

95% confidence interval.

enter your response here,enter your response here

(Round to one decimal place as needed.)

4)A gigantic warehouse stores approximately 60 million empty aluminum beer and soda cans. Recently, a fire occurred at the warehouse. The smoke from the fire contaminated many of the cans with blackspot, rendering them unusable. A statistician was hired by the insurance company to estimate p, the true proportion of cans in the warehouse that were contaminated by the fire. How many aluminum cans should be randomly sampled to estimate p to within

0.08 with 90% confidence?

The statistician should sample enter your response here cans to estimate the proportion that were contaminated by the fire to within 0.08 with 90% confidence.

5) According to a study, a cup of coffee contains an average of

115 milligrams (mg) of caffeine, with the amount per cup ranging from

60 to 195mg. Suppose you want to repeat the experiment in order to obtain an estimate of the mean caffeine content in a cup of coffee correct to within

7 mg with 90% confidence. How many cups of coffee would have to be included in your sample?

Part 1

The experiment must sample enter your response here cups of coffee in order to estimate the mean caffeine content in a cup of coffee correct to within

7 mg with90% confidence.

(Round up to the nearest whole number.)

6) Environmental engineers are using data collected by weather data centers to learn how climate affects the sea ice. Of 533 ice melt ponds studied in a certain region, 87 were classified as having "first-year ice". The researchers estimated that about 16% of melt ponds in the region have first-year ice. Estimate, with 90% confidence, the percentage of all ice-melt ponds in the region that have first-year ice. Give a practical interpretation of the results.

Question content area bottom

Part 1

Construct a 90% confidence interval around the sample proportion of ice melt ponds with first-year ice.

7)Researchers at a university designed and tested a speed-training program for junior varsity and varsity high school football players. Each in a sample of

38 high school athletes was timed in a 40-yard sprint prior to the start of the training program and timed again after completing the program. The decreases in times (measured in seconds) are listed in the accompanying table. [Note: A negative decrease implies that the athlete's time after completion of the program was higher than his time prior to training.] The goal of the research is to demonstrate that the training program is effective in improving 40-yard sprint times. Use these data to complete parts a and b below.

0.02	0.08	0.07	0.21	0.27	0.07	0.28	0.25	0.15
0.16	0.35	0.37	0.34	0.12	0.08	0.01	0.03	0.14
0.01	0.24	0.16	0.27	0.05	0.07	0.17	0.07	0.12
0.55	0.39	0.06	0.01	0.91	0.31	0.34	0.42	0.07
0.02	0.02

a. Find a 95% confidence interval for the true mean decrease in sprint times for the population of all football players who participate in the speed-training program. 8) The most common injury that occurs among mountain climbers is trauma to the lower extremity (leg). Consequently, rescuers must be proficient in immobilizing and splinting of fractures. The researchers examined the likelihood of needing certain types of splints. A Mountain Rescue study reported that there were 4 shaft splints needed among 332 live casualties. The researchers will use this study to estimate the proportion of all mountain casualties that require a femoral shaft splint. Complete parts a and b below.

Use Wilson's adjustment to find a 95% confidence interval for the true proportion of all mountain casualties that require a femoral shaft splint. Interpret the result.The 95% confidence interval is

(enter your response here,enter your response here).