3. The 2009 holiday retail season, which kicked off the day after Thanksgiving 2009, had been marked by somewhat lower consumer spending than was seen during the comparable period in 2008, probably due to the Great Recession. To get an estimate of consumer spending during this time, 436 randomly sampled American adults were surveyed. Based on this sample, a 95% confidence interval for the average daily consumer spending by American adults during the six-day period after Thanksgiving 2009 was found to be ($80.31, $89.11). Determine which of the following statements about this scenario are true and which are false. Give brief reasons for your answers. (a) If we considered all random samples of size 436 from the population of American adults in 2009, then for 95% of these samples, the sample mean (of the daily consumer spending during the six-day period after Thanksgiving 2009) would be between $80.31 and $89.11. (b) If we considered all random samples of size 436 from the population of American adults in 2009 and for each sample, we found a confidence interval for the population mean (of the daily consumer spending during the six-day period after Thanksgiving 2009), then 95% of these confidence intervals would contain the true population mean. (c) This confidence interval supports the assertion that the mean daily consumer spending among all American adults during the six-day period after Thanksgiving 2009 was at least $100. (d) The margin of error for this confidence interval is $4.40. In order to decrease the margin of error by half to 1$2.20, we would need to double the sample size to 872