1. According to an article in San Luis Obispo Tribune July 21, 2006 37% of the college freshman and 48% of the college seniors carry a credit balance from month to month. Suppose the reported percentages were based on random samples of 1000 college freshman and 1000 college seniors.
a) Construct a 90% confidence interval for the proportion of college freshman carry a credit card balance from month to month.
b) Construct a 90% confidence interval for the proportion of college seniors carry a credit card balance from month to month.
c) Explain why the 90% confidence intervals from a) and b) are not the same width.
2. In AP-AOL sports poll (Associated press, December 18, 2005), 394 of 1000 randomly selected U.S. adults indicated that they considered themselves to be a baseball fans. Of the 394 basketball fans, 272 stated that the thought the designated hitter rule should either be expanded to both baseball leagues or eliminated.
a) Construct 95% confidence interval for the proportion of those who consider themselves to be baseball fans.
b) Construct a 95% confidence interval for the proportion of those who consider themselves to be baseball fans that think the designated hitter rule should be expanded to both league or eliminated.
c) Explain why the confidence interval of parts a0 and b) are not of same width though both have a confidence level of 95%
3. In a study of 1710 schoolchildren in Australia (Herald Sun, October 27, 1994), 1060 children indicated that they normally watch TV before school in the morning. (Interestingly, only 35% of the parents said their children watched TV beforeschool!) Construct a 95% confidence interval for true proportion of Australian children who say they watch TV before school. What assumptions about the sample must be true before the method used to construct the interval valid.
4. In a survey conducted by Yahoo small business, 1432 of 1813 adults surveyed said they would alter their shopping habits if gas prices remain high. The is SRS data and normally distributed. Based on these survey data is it reasonable to conclude that more than three quarters of adults plan to alter their shopping habits if the gas price remain high.
5. Associated press reported 38 percent of all felons who were released from prison in 2003 landed back behind the bars by the end of the following year. Explain why it is not be necessary to carry out a hypothesis test to determine if the proportion of felons released in 2003 was less than 40%.
6. In 2004 poll of 5500 cell phone users , 20% indicated that had received commercial messages and ads on their cell phone. Is there sufficient evidence that the proportion of cell phone users who received commercial messages and ads was greater than the proportion of 0.13 reported for the previous year.
7. In a random sample of 117 female Hispanic drivers in Boston 68 were wearing seat belts. Does the data give good reason to conclude that more than half of Hispanic female drivers in Boston wear seat belts.