6.

In a study of 200 accidents that required treatment in an emergency room, 80 of the accidents occurred at home.

a) Find a 95% confidence interval for the population proportion of accidents treated in the emergency room that occurs at home.

b) Find a 99% confidence interval for the same value.

c) Find a 90% confidence interval for the same value.

d) Clearly explain the relationship between confidence level and the width of the confidence interval.

7.

USA Today reported on the results of an opinion poll in which adults were asked what one thing they are most likely to do when they are home sick with a cold or flu. In the survey, 63% said that they are most likely to sleep and 18% said that they would watch television. Although the sample size was not reported, typically opinion polls include approximately 1,000 randomly selected respondents.

a) Assuming a sample of 1,000 for this poll, construct a 95% confidence interval for the true percentage of all adults who would choose to sleep when they are at home sick.

b) If the true percentage of adults who would choose to sleep when they are at home sick is 70%, would you be surprised? Explain.

8.

Records show that the mean height of men in the United States (ages 20-29) is 69.9 inches. A random sample of 60 men in this age group is selected.

(a) What is the probability that the mean height for the sample is greater than 70 inches? Assume inches.

(b) Assume that the heights are normally distributed. Are you more likely to randomly select 1 man with a height less than 65 inches or are you more likely to select a sample of 15 men with a mean height less than 65 inches? Explain.

9.

Suppose a random variable x has a mean of 20 and a standard deviation of 5. Determine the mean and the standard deviation of the sample mean for each of the following sample sizes (Assume the population is infinite).

a) n = 35

b) n = 50

c)n = 75

c) What can you conclude about the standard deviation of the sample mean as n increases?

10.

In a city poll, 58% of the people prefer Candidate A. Suppose 45 people from this city were sampled.

(a) What is the mean of the sampling distribution of ?

(b) What is the standard error of ?

(c) What is the probability that 75% or more of this sample will prefer Candidate A?

(d) What is the probability that 65% or more of this sample will prefer some other candidate?