MATH 131 - Unit 3 Class Activity 08/16 1. If you make just one 90% confidence interval will it necessarily capture the population value you are estimating? ______________________________________________________ 2. If you make ten different 90% confidence intervals, how many of them do you think will capture the value? _______________________________________________________ 3. Consider the experiment of rolling a single six-sided dice. Let p be the population proportion (classical probability) of rolling a 2. What is the value for p ? ____________ Explain your reasoning. 4. ^p is a sample proportion (empirical probability) of 2's rolled. Use StatCrunch or Minitab to simulate the experiment of rolling a single die 200 times to find your sample statistic, ^p . ^p =__________________ StatCrunch Select Applets Select Games Select Fair Dice? Choose a company Click 100 rolls twice The percent over the bar at 2 is your sample ^p . Minitab Select Calc from the menu bar. Select Random Data. Select Integer. In the dialog box, make these entries: Generate 200 rows of data. Store in column C2. Minimum value: 1 Maximum value: 6 Click on OK. Select Stat from the menu bar. Select Tables. Select Tally. Type C2 in the Variable box. Check Counts. Click OK. Use the count next to 2 to find ^p 5. Construct a 99% confidence interval for p , the population probability of rolling a 2. Show your work, using the value from StatCrunch or Minitab listed in #4. 1 MATH 131 - Unit 3 Class Activity 08/16 6. Does your confidence interval contain the true value computed in #3? ______________ 7. If 100 students form a 99% confidence interval, how many of them would you expect to capture the true p value? _________________________________________ 8. If 1000 students form a 99% confidence interval, how many of them would you expect to contain the true p value? _________________________________________ 9. If StatCrunch is available, select Applets, Confidence Intervals, for a proportion. Choose the first option and fill in the value for p that you found in #3. Initial confidence level should be 0.99. Initial sample size should be 200. Compute How many of the intervals captured the population value (noted by the vertical line)? _____________ 10. Repeat the steps in #9 and change the confidence level to 0.90 (leave other values the same), what changed in the width of the intervals illustrated? Explain why. 11. Repeat the steps in #9 and change the sample size to 30 (leave other values the same), what changed in the width of the intervals illustrated? Explain why. 12. On the website Real Clear Politics poll data from a variety of polls is updated regularly. On June 20 the Monmouth University poll results showed that of 721 likely voters 49% would choose the Democratic candidate to win the November election. What is the margin of error for this poll? Is the election \"too close to call\"? Explain. 2 MATH 131 - Unit 3 Class Activity 08/16 3