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Open the corks ne Intervals for a Proportion wih p = 0.3 Applet or go to statcrunch and select Applets > confidence interval > for a proportion. 1. Exploring the role of confidence level: a) Construct 1,000 confidence interval with n= 100, p= 0.3. What proportion of the 9596 confidence interval included the population proportion, 0.3? Type/Copy your answer here. Construct another 1,000 confidence interval with n = 100, p = 0.3. What proportion of the 959% confidence interval included the population proportion, 0.3? Type/Copy your answer here. Did the same proportion of interval include the population proportion each time? What proportion did you expect to include the population proportion? Type your answer here. bj construct 1,000 confidence interval with n= 100, p= 0.3. What proportion of the 999% confidence interval included the population proportion, 0.3? Type/Copy your answer here. Construct another 1,000 confidence interval with n= 100, p = 0.3. what proportion of the 999% confidence interval included the population proportion, 0.3?" Type/Copy your answer here. Did the same proportion of interval include the population proportion each time? what proportion did you expect to include the population proportion in each part? Type your and wer here. 2. Exploring the role of sample see: a) Construct 1,000 confidence interval with * = 10, p = 0.3. what proportion of the 959% confidence interval included the population proportion, 0.3? Type/Copy your answer here. bj construct 1,000 confidence interval with * = 40, p = 0.3. what proportion of the 9596confidence interval included the population proportion, 0.3? Type/Copy your answer here. () construct 1,000 confidence interval with n = 100, p= 0.3. What proportion of the 959% confidence interval included the population proportion, 0.3? Type/Copy your answer here. d) Did the same proportion of interval include the population proportion in #23, #2b, and #Z:? Type your ard wer here. What proportion did you expect to include the population proportion in each part? Type your answer here What happens to the proportion of interval that include the population proportion as the sample sbe increases? why? Type your ard wer here. 3. Exploring the role of shape: a) Construct 100 confidence interval with p = 0.3, level of confidence = 0.95, and sample ibe = 100 Select one of the interval (denoted with a red line) that does not include the population proportion that & to the left of the population proportion, 0.3. If there are no such interval, repeat until there are. Scroll the mouse cursor over the interval. In the popup window, notice the value of the sample proportion. 1 = Type And wer Determine the number of standard errors the sample proportion & from the population proportion, 0.3, by computing: 1 - 0.3 3 =- (1 - 5) 10 0 Remember, the standard error is of = TL Type your answer here. bj From the same 100 confidence interval constructed in #3a, select one of the intervals that does not include the population proportion (red line) that i to the right of the population proportion. In the pop-up window, notice the value of the sample proportion. 1 = Type And wer Determine the number of standard errors the sample proportion & from the populationproportion, 0.3. Type your ard wer here. c) Are each of the sample proportions from #3a and #3b more than 1.96 standard errors from the population proportion? Explain why any sample proportion that & more than 1.96 standard errors from the population proportion will result in an interval that does not include the population proportion. Type your and wer here. Activity II: Exploring the Effects of Confidence Level, Sample Size, and Shape om Confidence Intervals for a Mean In the activity, you will use an applet to generate confidence interval for the population mean. You will use the results to understand what & meant by the confidence level and the role of sample see. You will abo explore how the shape of the original distribution affects the confidence interval. Open the confidence Intervals for a Meen (formal) Applet or go to Statcrunch and select Apple t > Confidence interval > for a mean. 1. Exploring the role of confidence level: a) Set the shape to normal with mean = 50and standard deviation = 10. b) Simulate at least 1,000 simple random samples from the population with . = 10. For 959% confidence, what proportion of the confidence interval included the population mean? Type/Copy your answer here. Simulate another 1,000 simple random samples from the population with . = 10. For 959% confidence, what proportion of the confidence interval included the population mean? Type/Copy your answer here. d) Did the same proportion of interval include the population mean in #1band #1c? Explain what the result implies. Type your answer here. What proportion did you expect to include the population mean? Explain any discrepancy. Type your answer here. 2. Exploring the role of sample see: 3) set the shape to normal with mean = 50and standard deviation = 10. bj simulate at least 1,000 simple random samples from the population with . = 10. For 959% confidence, what proportion of the confidence interval included the populationmean? Type/Copy your answer here. :) simulate 1,000 simple random samples from the population with * = 20. For 959% confidence, what proportion of the confidence interval included the population mean? Type/Copy your answer here. d) Simulate 1,000 simple random samples from the population with * = 40. For 959% confidence, what proportion of the confidence interval included the population mean? Type/Copy your answer here. compare the width of the interval for #2b -#20. Which interval have the larger width? Explain your response Type your and wer here. 3. Exploring the role of shape: Open the Confidence Intervalsfor a Me on (Ske wed) Applet or go to Statcrunchand selectApplets > confidence interval > fora mean. 3) Setthe shape toskewed right with * = 5, mean= 50, and standard deviation= 10. Simulate at least 1,000 simple random samples from this population. For959% confidence, what proportion of the confidence interval included the population mean? Type/Copy your and wer here. bj Setthe shape toskewed right with +3 = 10, mean= 50, and standard deviation= 10. Simulate at least 1,000 simple random samples from the population. For959% confidence, what proportion of the confidence interval included the population mean? Type/Copy your answer here. what proportion of intervals would you expect to include the population mean? Type your answer here. Is the proportion of simulated interval that included the population mean closer to what G expected than what was observed in #3a? Explain. Type your and wer here c) simulate obtaining random samples with a variety of sample sees. In your judgment, what sample see & needed in order for the proportion of intervals that include the mean to be equal to the proportion suggested by the level of confidence? Be sure to clearly describe your approach that led to your conclusion. Type/Copy your answer here