# 2) Bone density is measured using a z score.a) Find the probability the bone density is less than .845.b) Find the probability the bone density is in between -1.5 and 1.2.3) Disney World requires that people employed as mickey mouse characters must have a height between 56in and 62 in. Suppose mens heights are normally dis- tributed with a mean of 68.6in and a standard deviation of 2.8 in. Suppose women heights are normally distributed with a mean of 63.7in and a standard deviation of 2.9 in.a) Find the percentage of men meeting the height requirement.b) If the height requirement is changed to exclude the tallest 50% of men and the shortest 5% of men, what are the new height requirements?4) Out of the following, which are biased estimators of their corresponding popula- tion parameters?Sample mean, sample variance, sample range, sample standard deviation, sample proportion5) Samples of size n = 2 are randomely selected with replacement from the popula- tion consisting of 2, 3, and 10, where the values represent the number of people in households.5a) Find the range of each of the nine samples and summarize the data in the form of a probability distribution.5b) Compare the population range to the mean of the sample ranges.5c) Do the sample ranges target the population ranges?6) A Boeing airliner carries 200 passengers and has doors with heights of 72 inches. Heights of men are normally distributed with a mean 69 in and a standard deviation of 2.8 inches.6a) If a male passenger is randomely selected, find the probability that he can fit through the door without bending.6b) If half of the 200 passengers are men, find the probability that the mean height of the 100 men is less than 72.7c) Which are more relevant, results from parts a or b from question 3? Why?7d) Why might women be ignored in this study?8) Express the confidence interval (.437 , .529) in the form of pˆ±E (show the sample proportion and Margin of Error).9) In a research center poll, 73 % of of 3011 adults surveyed said they use the in- ternet. Construct a 95% confidence interval estimate of the proportion of all adults who use the internet. Is it correct for a reporter to write that 3/4 adults use the internet? Why or why not?10) Express the interval (19.853, 22.7) in the form of x̄ ± E (show the sample mean and Margin of Error) and in the form x̄ − E < μ < x̄ + E.11) Randomely selected students participated in an experiment to test their ability to determine when one minute (60 seconds) has passed. Forty students yielded a a sample mean of 58.3 seconds. Assume that σ = 9.5 seconds.What is the best point estimate for the mean for all student times?Construct a 99 % confidence interval estimate for the population mean for all stu- dents.Is it likely that their mean have an estimate that is reasonably close to 60 seconds?12) What sample size is needed to estimate the mean white blood cell count for the population of adults in the U.S? Assume you want a 99% confidence that the sample mean is within .2 of the population mean. The population standard deviation is 2.5.13) Find the p-value for a right tailed test with a z-score = 2.5. Use a .05 significance level to state the conclusion of the Null Hypothesis (this is a pleasant warm-up for problems going forward).14) In a study of 420,095 Danish cell phone users, 135 subjects developed cancer of the brain. Test the claim that cell phone users develop cancer of the brain at a rate different from the rate of .0340% for people who do not use cell phones. Use a .005 signigicance level. Should cellphone users be concerned?15) A recently televised broadcast of 60 Minutes had a 15 share, meaning that among 5000 monitored households with TV sets in use, 15% of them were tuned into 60 minutes. Use a .01 significance level to test the claim that out of the TV sets in use, less than 20% were tuned to 60 minutes.16) A simple random sample of 24 filtered 100 mm cigarettes is obtained and the tar content of each cigarette is mentioned. The sample has a mean of 13.2 mg and a standard deviation of 3.7 mg. Use a .05 level of significance to test the claim that the mean tar content of 100 cigarettes is less than 21.2 mg (which is the mean for king size cigarettes). What do the results suggest about the effectiveness of the filters?17) In an experiment, 16% of 734 subjects treated with viagra experienced headaches. In the same experiment, 4% of 725 subjects given a placebo experienced headaches. Use a .01 level of significance to test the claim that the proportion of headaches is greater for those treated with viagr

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2) Bone density is measured using a z score.
a) Find the probability the bone density is less than .845.

b) Find the probability the bone density is in between -1.5 and 1.2.

3) Disney World requires that people employed as mickey mouse characters must have a height between 56in and 62 in. Suppose mens heights are normally dis- tributed with a mean of 68.6in and a standard deviation of 2.8 in. Suppose women heights are normally distributed with a mean of 63.7in and a standard deviation of 2.9 in.

a) Find the percentage of men meeting the height requirement.

b) If the height requirement is changed to exclude the tallest 50% of men and the shortest 5% of men, what are the new height requirements?

4) Out of the following, which are biased estimators of their corresponding popula- tion parameters?

Sample mean, sample variance, sample range, sample standard deviation, sample proportion

5) Samples of size n = 2 are randomely selected with replacement from the popula- tion consisting of 2, 3, and 10, where the values represent the number of people in households.

5a) Find the range of each of the nine samples and summarize the data in the form of a probability distribution.

5b) Compare the population range to the mean of the sample ranges.

5c) Do the sample ranges target the population ranges?

6) A Boeing airliner carries 200 passengers and has doors with heights of 72 inches. Heights of men are normally distributed with a mean 69 in and a standard deviation of 2.8 inches.

6a) If a male passenger is randomely selected, find the probability that he can fit through the door without bending.

6b) If half of the 200 passengers are men, find the probability that the mean height of the 100 men is less than 72.

7c) Which are more relevant, results from parts a or b from question 3? Why?

7d) Why might women be ignored in this study?

8) Express the confidence interval (.437 , .529) in the form of pˆ±E (show the sample proportion and Margin of Error).

9) In a research center poll, 73 % of of 3011 adults surveyed said they use the in- ternet. Construct a 95% confidence interval estimate of the proportion of all adults who use the internet. Is it correct for a reporter to write that 3/4 adults use the internet? Why or why not?

10) Express the interval (19.853, 22.7) in the form of x̄ ± E (show the sample mean and Margin of Error) and in the form x̄ − E < μ < x̄ + E.

11) Randomely selected students participated in an experiment to test their ability to determine when one minute (60 seconds) has passed. Forty students yielded a a sample mean of 58.3 seconds. Assume that σ = 9.5 seconds.
What is the best point estimate for the mean for all student times?

Construct a 99 % confidence interval estimate for the population mean for all stu- dents.

Is it likely that their mean have an estimate that is reasonably close to 60 seconds?

12) What sample size is needed to estimate the mean white blood cell count for the population of adults in the U.S? Assume you want a 99% confidence that the sample mean is within .2 of the population mean. The population standard deviation is 2.5.

13) Find the p-value for a right tailed test with a z-score = 2.5. Use a .05 significance level to state the conclusion of the Null Hypothesis (this is a pleasant warm-up for problems going forward).

14) In a study of 420,095 Danish cell phone users, 135 subjects developed cancer of the brain. Test the claim that cell phone users develop cancer of the brain at a rate different from the rate of .0340% for people who do not use cell phones. Use a .005 signigicance level. Should cellphone users be concerned?

15) A recently televised broadcast of 60 Minutes had a 15 share, meaning that among 5000 monitored households with TV sets in use, 15% of them were tuned into 60 minutes. Use a .01 significance level to test the claim that out of the TV sets in use, less than 20% were tuned to 60 minutes.

16) A simple random sample of 24 filtered 100 mm cigarettes is obtained and the tar content of each cigarette is mentioned. The sample has a mean of 13.2 mg and a standard deviation of 3.7 mg. Use a .05 level of significance to test the claim that the mean tar content of 100 cigarettes is less than 21.2 mg (which is the mean for king size cigarettes). What do the results suggest about the effectiveness of the filters?

17) In an experiment, 16% of 734 subjects treated with viagra experienced headaches. In the same experiment, 4% of 725 subjects given a placebo experienced headaches. Use a .01 level of significance to test the claim that the proportion of headaches is greater for those treated with viagr

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