1) A manufacturer of cell phones batteries wants to estimate the useful life of its battery (in thousands of hours). The estimate needs to be within 0.10 (100 hours). Assuming a 95% level of confidence and a standard deviation of the useful life of the battery is 0.90 (900 hours). Determine the sample size. [Hint: First, determine the maximum allowable error from the above information and then apply the formula for estimating the sample size]
2) Historically, the proportion of adults over the age of 24 who smoke has been 0.30. A more recent sample of 500 adults revealed only 25% of those sampled smoked. Develop a 98% confidence interval for the proportion of adults who currently smoke. Is this confidence interval less than the historic average? [Hint: Is the population standard deviation known?]
3) A local radio station provides morning drive-time news. They also encourage listeners to weigh in on topics. This morning the question was: how many hours do children under 12 years of age watch TV per day. Five callers responded that their children watched the following number of hours of TV last night:
| Caller |
TV Hours |
| 1 |
3.0 |
| 2 |
3.5 |
| 3 |
4.0 |
| 4 |
4.5 |
| 5 |
3.0 |
a) What is the mean?
b) What is the standard deviation? [Remember: this is a small sample.)
c) What is the range of hours of TV watched?