UNIT 4 show all work please!! So that I might try to understand the process better Thank you. 1. If = 103, =27, n = 31, construct a 99% confidence interval estimate of the population mean, . (Round two decimal places as needed) ____ ____ 5. 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 bottlingcompany'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 0.986 gallon. Complete parts (a) through (d). a. Construct a 95% confidence interval estimate for the population mean amount of water included in a 1-gallon bottle. 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 95% 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 Overbar X is normally distributed when n is large. In this case, the value of n is large. d. Construct a 90% confidence interval estimate. How does this change your answer to part (b)? 6. A marketing researcher wants to estimate the mean amount spent($) on a certain retail website by members of thewebsite's premium program. A random sample of 90 members of the website's premium program who recently made a purchase on the website yielded a mean of $1900 and a standard deviation of $350. a. Construct a 95% confidence interval estimate for the mean spending for all shoppers who are members of thewebsite's premium program. ____ ____ b. Interpret the interval constructed in (a). 2. A survey of nonprofit organizations showed that online fundraising has increased in the past year. Based on a random sample of 50 nonprofits, the mean one-time gift donation in the past year was UNIT 4 show all work please!! So that I might try to understand the process better Thank you. $33, with a standard deviation of $7. a. Construct a 90% confidence interval estimate. For the population one-time gift donation. b. Interpret the interval constructed in (a). The quality improvement team can be 90% confident that the new population mean turnaround time is contained within the confidence interval. 3. IF n = 100 and X=40, construct a 959% confidence interval estimate of the population proportion. ____ ____ (Round to four decimal places as needed) 4. If you want to be 95% confident of estimating the population proportion to within a sampling error of 0.03, what sample size is needed? (Round to the nearest integer.) 5. If you want to be 95% confident of estimating the population proportion to within a sampling error of 0.06 and there is historical evidence that the population proportion is approximately 0.36, what sample size is needed? (Round to the nearest integer.) A sample size of ___ is needed 6. If a light bulb manufacturing company wants to estimate, with 99% confidence, the mean life of compact fluorescent light bulbs to within 250 hours and also assumes that the population standard deviation is 1000 hours, how many compact fluorescent light bulbs need to be selected? n= ___ (Round to the nearest integer.) 7. 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 22 minutes. The executive wants the estimate, with 99% confidence, the mean weekly amount of time to within 6 minutes. a. What sample size is needed? (Round to the nearest integer.) b. If 95% confidence is desired, how many consumers need to beselected? (Round to the nearest integer.) a) The sample size required for 99% confidence is ____ b) The sample size required for 95% confidence is ____ UNIT 4 show all work please!! So that I might try to understand the process better Thank you. 8. In a study of 405 nonprofits nationwide, 86 indicated that turnover has been the biggest employment challenge at their organization. a. Construct a 95% confidence interval for the population proportion of nonprofits that indicate turnover as the biggest employment challenge at their organization. ____ ____ (Type integers or decimals. Round to three decimal places as needed.) b. Interpret the interval constructed in part (a) 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 c. If you wanted to conduct a follow up study to estimate the population of non-profits that include turnover as the biggest employment challenge at their organization to within 0.02 with 95% confidence. How many nonprofits would you survey? (Round up to the nearest integer.) 9. What prevents consumers from sharing data with retailers? A recent survey found that 27% of consumers responded \"breaches of consumer data." Complete parts (a) through (c) below. a. To conduct a follow-up study that would provide 99% confidence that the point estimate is correct to within 0.02 of the populationproportion, how many consumers need to be sampled? n= ____ (Round up to the nearest integer.) b. To conduct a follow-up study that would provide 99% confidence that the point estimate is correct to within 0.04 of the population proportion, how many need to be sampled? n= ___ (Round up to the nearest integer.) c. Compare the results of (a) & (b) The sample size needed for part(a) is larger than the sample size needed for part(b), so as the acceptable samplingerror, e,increases, the sample size needed decreases