A random sample of 1200 Freshmen at UGA were asked if they had applied for student football tickets. The proportion who answered yes was 0.86. The standard error of this estimate is 0.010. (a) Find the margin of error for a 95% confidence interval for the population proportion who applied for football tickets. :] (3 decimal places) (b) Construct the 95% confidence interval. Lower Limit (3 decimal places) Upper Limit (3 decimal places) (c) Since the sample was randomly selected, will this confidence interval be valid? 0 None of these. 0 Yes because at least one of (1200)*(0.86) and (1200)*(1 - 0.86) is greater than 15. 0 Yes because both (1200)*(0.86) and (1200)*(1 - 0.86) are greater than 15. 0 Yes because at least one of (1200)*(O.86) and (1200)*(1 - 0.86) is greater than 30. 0 Yes because the sample size is greater than 30. (d) Using the above confidence interval, what can you say about the true population proportion? Q If we were to take many samples like this, and calculate a 95% confidence interval for each one, approximately 95% of these intervals would contain the true population proportion. Q We are 95% confident that the sample proportion is in this interval. When a truckload of apples arrives at a packing plant, a random sample of 200 apples are selected and examined for bruises and other defects. In reality, 15% of the apples on a particular truck are bruised or otherwise unsatisfactory. (a) How many standard errors away from 0.15 would you need to go to contain 89% of the sample proportions of bad apples you might expect to find? (3 decimal places) (b) Suppose you were going to construct an 89% confidence interval from this population. What critical value should you use? (3 decimal places) The 2002 General Social Survey asked, "What do you think is the ideal number of children for a family to have?" The 508 females who responded had a mean of 3.03, and standard deviation of 1.79. The 95% confidence interval is (2.87, 3.19). (a) What is the sample statistic? (2 decimal places) (b) Find the standard error. (3 decimal places) (c) Using the confidence interval, what can you say about the true population mean? 0 We are 5% confident that the true mean ideal number of children for a family to have is between 2.87 and 3.19. Q We are confident that 95% of Americans think that the true mean ideal number of children for a family to have is between 2.87 and 3.19. Q We are confident that, 95% of the time, the true mean ideal number of children for a family to have is between 2.87 and 3.19. Q We are 95% confident that the true mean ideal number of children for a family to have is between 2.87 and 3.19. (d) According to this interval, is it plausible that the population mean is 2? Explain. O Yes, 2 is not in this interval. O No, 2 is in this interval. O Yes, 2 is in this interval. O No, 2 is not in this interval. (e) If we were to conduct a hypothesis test of H0: M = 2 vs. Ha: H 2, what could we say based off the above interval? C] The p-value is greater than .05 C] We would reject the null hypothesis C] None of the other conclusions could be made C] We would not reject the null hypothesis C] The p-value is less than .05