1. A newspaper 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 the flu. In the survey, 65% said that they are most likely to sleep and 19% 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 size 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 homesick.
The 95% confidence interval is ( , ).
(Round to the nearest hundredth as needed.)
2. Suppose data collected by observers at randomly selected intersections across the country revealed that in a sample of 500 drivers, 450 were using their cell phone.
a. Give a point estimate of p, the true driver cell phone use rate (that is, the true proportion of drivers who are using their cell phone while driving).
b. Compute a 95% confidence interval for p.
c. Give a practical interpretation of the interval, part b.
a. A point estimate for p is ??.
b. The 95% confidence interval for p is ( , ).
(Round to two decimal places as needed.)
3. A company tests all new brands of golf balls to ensure that they meet certain specifications. One test conducted is intended to measure the average distance traveled when the ball is hit by a machine. Suppose the company wishes to estimate the mean distance for a new brand to within 1.4 yards with 95% confidence. Assume that past tests have indicated that the standard deviation of the distances the machine hits golf balls is approximately 10 yards. How many golf balls should be hit by the machine to achieve the desired accuracy in estimating the mean?
The machine should hit ??? golf balls to achieve the desired accuracy in estimating the mean.
(Round up to the nearest golf ball.)