Having trouble with this these problems, Thanks in advance.
1)
In a study at 422 nonprots nationwide, 34 indicated that turnover has been the biggest employment challenge at their organization. Complete parts (a) through (c). a. construct a Bb'ilh condence Interval ror tne population proportlon ot nonprots that Indicate turnover as the biggest employment challenge at tnelr organlzatlon. s r: 5 (Type integers or decimals. Round to three decimal places as needed.) b. Interpret the interval mnstructed in part (a). Choose the correct answer below. 0 A. With 5% condence. the proportion of nonprots that indicate turnover as the biggest employment challenge at their organization in the sample is in this interval. 0 B. With 5% condence. the proportion of nonprots that indicate turnover as the biggat employment challenge at their organization in the population is in this interval. 0 C. With 95% condence, the proportion ofnonprots that indicate tumover as the biggest employment challenge at their organization in the sample is in this interval. 0 D. With 95% condence, the proportion ofnonprots that indicate tumover as the biggest employment challenge at their organization in the population is in this interval. 6. If you wanted to conduct a follow-up study to estimate the population proportion of nonprots that indicate tumover as the biggest employment challenge at their organization to within 1 0.02 with 95% condence, how many nonprots would you survey? A sample of ii nonprots should be surveyed. (Round up to the nearest intlecer.i The qualityr mntml manager at a light bulb factoryr needs to Etimate the mean life of a large shipment of light bulbs. The standard deviation is 98 hours. A random sample of 49 light bulbs indicated a sample mean life of 350 hours. Complete parts (a) through (d) below. a. Construct a 95% condence interval estimate for the population mean life of light bulbs in this shipment. The 95% condence interval estimate is from a lower limit of hours to an upper limit of hours. (Round to one decima place as needed.) b. Do you think that the manufacturer has the right to state that the lightbulbs have a mean life of 410 hours? Explain. Based on the sample data. the manufacturer i the right to state that the Iightbulbs have a mean life of 410 hours. A mean of 410 hours is 7 standard errors Y the sample mean, so it is Y that the lightbulbs have a mean life of 410 hours. 0. Must you assume that the population llght bulb lll'S I5 normally UiBiJ'IDUIeG'f explain. 0 A. Yes, the sample size is too large for the sampling distribution of the mean to be apprmdmately normal bythe Central Limit Theorem. 0 B. No, since o is known and the sample size is large enough, the sampling distribution oi the mean is approximately normal by the Central Limit Theorem. 0 C. No, since u is known. the sampling distribution of the mean does not need to be approximate y normally distributed. 0 D. Yes, the sample size is not large enough for the sampling distribution oi the mean to be approximately normal by the Central Limit Theorem. d. Suppose the standard deviation changes to 77 hours. What are youranswers in (a) and (b)? The 95% condence interval estimate would be from a lower limit of hours to an upper limitoi hours. (Round In one decimal place as needed.) Based on the sample data and a standard deviation of T? hoursI the manufacturer 7 the right to state that the lightbulbs have a mean life of410 hours. A mean of 410 hours is 1' standard errors Y the sample mean. so it is Y that the lightbulbs have a mean lite of410 hours. A market researcher Elects a simple random sample of n = 100 users of a social media website from a population of ever 100 million registered users. After analyzing the sample, she states that she has 95% condence that the mean time spent on the site per day is between 15 and 5? minutes. Explain the meaning ot'this statement. Choose the correct answer below. 0 A. One is 95% condent that the true mean time all registered users spend on the site per day is between 15 and 57 minutes. (Q B. There is a 95% ohanoe thata randomly selected registered user spends between 15 and 57 minut on the site per day. O c. During any given day there is a 95% chance that the mean time all registered users spent on the site was between 15 and 5? minutes. 0 D. Of the over 100 million registered users. 95% of them spend between 15 and 57 minutes on the site perday. According to a social media blog, time spent on a certain social nemorning website has a mean of 24 minutes per visit. Assume that time spent on the social networking site per visit is normally distributed and that the standard deviation is 5 minutes. Complete parts (a) through (d) below. a. fyou select a random sample of 16 sessions. what is the probability that the sample mean is between 23.5 and 24.5 minutes? (Round to three decimal places as needed.) b. If you select a random sample of16 sessions, what is the probabilityr that the sample mean is between 23 and 24 minut? (Round to three decimal places as needed.) c. fyou select a random sample of 144 sessions. what is the probability that the sample mean is between 23.5 and 24.5 minutes? (Round to three decimal places as needed.) d. Explain the ditferenoe in the results of (a) and (c). d. Explain the differenoe in the resuits of (a) and (ct The sample size in (c) is greater than the sample size in (a). so the standard error of the mean (or the standard deviation of the sampling distribution) in {e} is Y than in (a). As the standard error V values become more concentrated around the mean. Therefore, the probability that the sample mean wiil fall in a region that includes the population mean will aiways when the sampie size increases. Y
