Are you annoyed with spam e-mail? Suppose a random sample of 200 Penn State students was asked this question of which 80% said that they are annoyed. From the provided information we can find the following:
sample percent = 80% (sample proportion = .80)
standard deviation (S.D.) = .03
a. Set up the calculation of a 95% confidence interval to estimate the population proportion of Penn State students who are annoyed by spam e-mail? (Hint: refer to Example 12.5)
b. Knowing that the margin of error = .06 or 6%, write out a one-sentence interpretation of the margin of error.
c. The 95% confidence interval to estimate the population proportion of Penn State students who are annoyed by spam e-mail is (.74 to .86). Write out a one-sentence interpretation of this confidence interval.
d. What type of data is used in this example-categorical or measurement?
e. What would happen to the size of the margin of error or confidence interval if the level of confidence were instead 99.7%? Explain.
8. Explain what will happen to the width of a confidence interval (increase, decrease, or remain the same) as a result of each of the following changes:
a. Population size is doubled from 5 million to 10 million
b. Confidence level lowered from 98% to 90%
c. Sample size is doubled from 500 to 1000
9. A sample of 200 students in a Stat class were asked "How long did you sleep last night?" The results are found below.
sample mean = 6.4 hours
S.D. = 1.6 hours
standard error (S.E.) = .11 hours
sample size (n) = 200
a. Set up the calculation of a 95% confidence interval to estimate the population mean number of hours slept last night.
b. Knowing that the margin of error = .22, write out a one-sentence interpretation of the margin of error.
c. The 95% confidence interval to estimate the population mean number of hours slept last night is (6.18 to 6.62) hours. Write out a one-sentence interpretation of this confidence interval.
d. What type of data is used in this example?
e. What would happen to the size of the margin of error or confidence interval if the level of confidence were instead 68%? Explain
10. A 95% confidence interval for the proportion of women that have ever dozed off while driving is 0.07 to 0.14. For men, a 95% confidence interval for the proportion that have ever dozed off while driving is 0.19 to 0.25. Assume both intervals were computed using large random samples.
a. What conclusion can be made about the two population proportions that have dozed off while driving? Why?
b. Rewrite each confidence interval in terms of percents rather than proportions. Does the conclusion remain the same? Explain.
c. The two samples are which of the following: two independent or two dependent (matched pairs)?
d. What type of data is found in this problem-categorical or measurement?
e. Would the conclusion remain the same if the two confidence intervals had instead been calculated at 90% confidence? Explain.