A bottled water distributor wants to estimate the amount of water contained in 1-gallon bottles purchased from a nationally known water bottling company. The water bottling company's specifications state that the standard deviation of the amount of water is equal to 0.02 gallon. A random sample of 50 bottles is selected, and the sample mean amount of water per 1-gallon bottle is 0.969 gallon. Complete parts (a) through (d). a. Construct a 99% confidence interval estimate for the population mean amount of water included in a 1-gallon bottle. 0.96171 sus 0.97629 (Round to five decimal places as needed.) b. On the basis of these results, do you think that the distributor has a right to complain to the water bottling company? Why? Yes, because a 1-gallon bottle containing exactly 1-gallon of water lies outside the 99% confidence interval. c. Must you assume that the population amount of water per bottle is normally distributed here? Explain. A. No, because the Central Limit Theorem almost always ensures that X is normally distributed when n is small. In this case, the value of n is small. B. No, because the Central Limit Theorem almost always ensures that X is normally distributed when n is large. In this case, the value of n is large. O C. Yes, because the Central Limit Theorem almost always ensures that X is normally distributed when n is large. In this case, the value of n is small. D. Yes, since nothing is known about the distribution of the population, it must be assumed that the population is normally distributed. d. Construct a 95% confidence interval estimate. How does this change your answer to part (b)? SHE (Round to five decimal places as needed.)Assuming that the population is normally distributed, construct a 95% confidence interval for the population mean for each of the samples below. Explain why these two samples produce different confidence intervals even though they have the same mean and range. Sample A: 1 2 2 3 6 7 7 8 Full data set Sample B: 1 2 3 4 5 6 7 8 Construct a 95% confidence interval for the population mean for sample A. 2.18 sus 6.82 (Type integers or decimals rounded to two decimal places as needed.) Construct a 95% confidence interval for the population mean for sample B. (Type integers or decimals rounded to two decimal places as needed.)In a survey of 3,890 adults concerning complaints about restaurants, 1,442 complained about dirty or ill-equipped bathrooms and 1,214 complained about loud or distracting diners at other tables. Complete parts (@) through (c) below. a. Construct a 90% confidence interval estimate of the population proportion of adults who complained about dirty or ill-equipped bathrooms. 0.3580 Exs 0.3834 (Round to four decimal places as needed.) b. Construct a 90% confidence interval estimate of the population proportion of adults who complained about loud or distracting diners at other tables. Exs (Round to four decimal places as needed.)An advertising executive wants to estimate the mean weekly amount of time consumers spend watching traditional television daily. Based on previous studies, the standard deviation is assumed to be 26 minutes. The executive wants to estimate, with 99% confidence, the mean weekly amount of time to within 1 3 minutes. a. What sample size is needed? b. If 95% confidence is desired, how many consumers need to be selected? a. The sample size required for 99% confidence is 498 (Round up to the nearest integer.)In a study of 421 nonprofits nationwide, 88 indicated that turnover has been the biggest employment challenge at their organization. Complete parts (a) through (c). a. Construct a 95% confidence interval for the population proportion of nonprofits that indicate turnover as the biggest employment challenge at their organization. 0.170 SIS 0.248 (Type integers or decimals. Round to three decimal places as needed.) b. Interpret the interval constructed in part (a). Choose the correct answer below. O A. With 5% confidence, the proportion of nonprofits that indicate turnover as the biggest employment challenge at their organization in the population is in this interval. B. With 95% confidence, the proportion of nonprofits that indicate turnover as the biggest employment challenge at their organization in the population is in this interval. O C. With 95% confidence, the proportion of nonprofits that indicate turnover as the biggest employment challenge at their organization in the sample is in this interval. O D. With 5% confidence, the proportion of nonprofits that indicate turnover as the biggest employment challenge at their organization in the sample is in this interval. c. If you wanted to conduct a follow-up study to estimate the population proportion of nonprofits that indicate turnover as the biggest employment challenge at their organization to within 1 0.02 with 95% confidence, how many nonprofits would you survey? A sample of nonprofits should be surveyed. (Round up to the nearest integer.)