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[-/1 Points] DETAILS ILLOWSKYINTROSTAT1 8.3.130.HW. On a certain day, Gallup reported that of the 1,006 people surveyed, 77%% of U.S. workers believe that they will continue working past retirement age. The confidence level for this study was reported at 95% with a 23%% margin of arron. Part (a) Part (b) Part (c) B Part (6) Calculate the error bound based on the information provided. (Round your answer to three decimal places.) B Part (a) Compare the error bound in part (o) to the margin of error reported by Gallup. Explain any differences between the values. This answer has not bean graded you Part In Create a confidence interval for the results of this study. (Round your answers to three decimal places.) B Part lol A reporter is covering the release of this study for a local news station. How should she explain the confidence interval to her audience? O We can say with 95% confidence that the percentage of adult U.S. workers in this sample who expect to continue working beyond retirement age is between the lower and upper bounds of the confidence interval O We can say with 95% confidence that the odds that an adult worker in the U.S. will continue working beyond retirement age is between the lower and upper bounds of the confidence interval. O We can say with 85% confidence that the percentage of all adult workers across the U.S. who expect to continue working beyond retirement age is between the lower and upper bound of the confidence interval We can say with 85% confidence that the percentage of adults workers across the U.S. who wil work beyond retirement age is between the lower and upper bounds of the confidence interval.A camp director is interested in the mean number of letters each child sends during his or her camp session. The population standard deviation is known to be 2.2. A survey of 20 campers is taken. The mean from the sample in 7.1 with a sample standard deviation of 2.7. 8 Part (b) Doing the random variables X and X in words. O Xis me number of lubers a single camper will send home. and Ris the mean number of loners cast home from a sample of 20 campan O X is the mean number of letters sent home from a san ra, and X in the number of lasers a single camper wil sand home. O Xis the mean number of campers who send letters home from a sample of 20 camps, and Xis the number of campers who send letters home. O X is the number of campers who send letters home, and * is the mean number of campers who mand laters home from a sample of 20 camps. Which dubution should you use for this problem? Explain your choice. The standard mean is given. The Student's A dubution should be used because the sample mean is smaller than 10 The Handed normal caribetion should be win the population standard drevion is known. The Student's debuton should be used because the sample standard deviation is given. 8 Part id Construct a BOW confidence interval for the population mean number of letters campers sand home. Of Some the confidence interval (Round your users to two decimal places.) () Sketch the graph. (Round your answers to two decimal places ) C.L. = X () Calovate the error bound. (Round your answer to too decimal places. ) What will happen to the over bound and con are surveyed? Why ? Q The confidence interval wil increase decreases variability, which means a larger interval will be needed to caption the true population mean. The confidence interval wil doorearn soreases variability which means a sealer interved will be enough to captain to be population coin. Q The coaldance interval will inoramon in nice, Bad inorthin in sample sice increases variability, which means a light interval wil be needed to caphe's the true population main. confidence interval wil decrease in nice, because an increase in sample size increases variability, which means a smaller interval will be anough to capture the true population meanPart (d) Construct a 90% confidence interval for the population mean time to complete the tax forms. (1) State the confidence interval. (Round your answers to two decimal places.) () Sketch the graph. (Round your answers to two decimal places.) C.L. = NIR X () Calculate the error bound. (Round your answer to two decimal places.) B Part (e) If the firm wished to increase its level of confidence and keep the error bound the same by taking another survey. what change should it make? O It should increase the number of people surveyed. It should decrease the number of people surveyed. B Part (n) If the firm did another survey. kept the error bound the same. and only surveyed 40 people. what would happen to the level of confidence? Why? O The level of confidence would be smaller because we have collected a smaller sample, obtaining less accurate information. O The level of confidence would be larger because we have collected a smaller sample. obtaining less accurate information. O There would be no change. B Part (ol Suppose that the firm decided that it needed to be at least 60% confident of the population mean length of time to within one hour. How would the number of people the firm surveys change? Why? The number of people surveyed would decrease because more accurate information requires a smaler sample. O The number of people surveyed would inc more accurate information requires a larger sample There would be no change.Suppose that an accounting firm does a study to determine the time needed to complete one person's tax forms. It randomly surveys 100 people. The sample mean is 30.3 hours. There is a known population standard deviation of 6-3 hours, The population distribution is assumed to be normal NOTE: D you are using a Student's F-distribution, you may assume that the underlying population is normally distributed. (In general, you must first prove that aurumption, though.) Q Xin the tome needed to complete one person's tax forms, and Xis the mean time needed to complete tax forma from a sample of 100 curioman. O Rinthe member of too forms that an spooning how compistes, and Xi the moon member of tax forms that an apppunting tom cospires. 8 Partici Which siptribution whould you win for pis problem? (Round your answers to tag decimal places) Explain your the da The standard normal difftribution should be used because the mean in givin.B) Part (d) Suppose we want to lower the sampling error. What is one way to accomplish that? O decrease the level of confidence O decrease the standard deviation decrease the sample size O increase the level of confidence Part (e) The sampling error given by Yankelovich Partners, Inc. (which conducted the poll) is 13%%. Explain what the 13%% represents. ) It means that the stated population proportion may be off by 3 percentage points due to errors in the survey. This means the interval created around the point estimate of 20% is 17%-23%. The stated population proportion is within 3 percentage points of the true population proportion. O This means that there is a 3% chance that the stated population proportion is not correct. O) This means that the company is between 92% and 98% confident that the population proportion falls within the confidence interval.telephone poll of 1.000 adult Americans was reported in an hus of Time Magazine. One of the questions asked was "what in the main problem facing the country?" Twenty percent animared "crime." We are Interested in the population proportion of adult American whatsal that crime in the main problem. proportion of people who think there are problema facing the country Explain your choice Q The reded x C.L. =0 = PPart (d) Construct a 95% confidence interval for the population mean worth of coupons. (i) State the confidence interval. (Round your answers to two decimal places.) (ii) Sketch the graph. C.L. = = X (ili) Calculate the error bound. (Round your answer to two decimal places.) Part (e) If many random samples were taken of size 14, what percent of the 95% confidence intervals constructed should contain the population mean worth of coupons? 19% Explain why. O There is a 95% chance that these samples will contain the population average worth of coupons. O A 95% confidence interval means that 95% of all possible samples will result in an interval that includes the population average worth of coupons. O A 95% confidence interval means that 100% of actual samples will result in an interval that includes the population average worth of coupons. The more samples you take. the more likely they will all contain the population average worth of coupons.A survey of the mees number of cente all that coupons give was conducted by readonly surveying one coupon per pegs from the coupon sections of a recent San Jose Memory Near. The following dets were collected 250 706 356 454 304: 356 601 40# 306 354 51.34: 406 454 40. Ammame the ww simately