You may need to use the appropriate appendix table or technology to answer this question. A magazine conducts an annual survey in which readers rate their favorite cruise ship. All ships are rated on a 100-point scale, with higher values indicating better service. A sample of 34 ships that carry fewer than 500 passengers resulted in an average rating of 85.58, and a sample of 44 ships that carry 500 or more passengers provided an average rating of 81.90. Assume that the population standard deviation is 4.55 for ships that carry fewer than 500 passengers and 3.97 for ships that carry 500 or more passengers. (a) What is the point estimate of the difference between the population mean rating for ships that carry fewer than 500 passengers and the population mean rating for ships that carry 500 or more passengers? (Use smaller cruise ships larger cruise ships.) 3.68 (b) At 95% condence, what is the margin of error? (Round your answer to two decimal places.) (c) What is a 95% condence interval estimate of the difference between the population mean ratings for the two sizes of ships? (Use smaller cruise ships larger cruise ships. Round your answers to two decimal places.) to | You may need to use the appropriate appendix table or technology to answer this question. Suppose that you are responsible for making arrangements for a business convention and that you have been charged with choosing a city for the convention that has the least expensive hotel rooms. You have narrowed your choices to Atlanta and Houston. The file named Hotel contains samples of prices for rooms in Atlanta and Houston that are consistent with a SmartMoney survey conducted by Smith Travel Research. Because considerable historical data on the prices of rooms in both cities are available, the population standard deviations for the prices can be assumed to be $20 in Atlanta and $25 in Houston. Based on the sample data, can you conclude that the mean price of a hotel room in Atlanta is lower than one in Houston? State the hypotheses. (Let u, = mean hotel price in Atlanta and let My = mean hotel price in Houston.) O Ho: M1 - H2 > o Ha: M1 - M2 = 0 Ho: M1 - H2 20 O Ha: M1 - M2 0 Ha: Hd SO O Ho: Hd SO Ha: Hd = 0 O Ho: MJ SO Ha: Hd > O O Ho: Md # 0 Hai Hd = 0 Calculate the value of the test statistic. (Round your answer to three decimal places.) Calculate the p-value. (Round your answer to four decimal places.) p-value = State your conclusion. O Do not reject Ho. There is insufficient evidence to conclude that seeing the commercial improves the mean potential to purchase. O Do not Reject Ho. There is sufficient evidence to conclude that seeing the commercial improves the mean potential to purchase. O Reject Ho. There is sufficient evidence to conclude that seeing the commercial improves the mean potential to purchase. O Reject Ho. There is insufficient evidence to conclude that seeing the commercial improves the mean potential to purchase.You may need to use the appropriate technology to answer this question A travel association reported the domestic airfare (in dollars) for business travel for the current year and the previous yean Below is a sample of 12 ighs with their domestic airfares shown for both years, CIII'I'GIII Previous Year Vell- 345 303 526 463 420 450 216 206 285 275 405 432 635 585 710 650 605 545 517 547 570 495 610 580 (a) Formulate the hypotheses and test for a signicant increase In the mean domestic airtare for business travel for the one-year period. Calculate the test statistic (Use current year airfare previous year airfare. Round your answer to three decimal places.) : calculate the pvaluet (Round your answer to four decimal places.) Using a 0.05 level of signicance, what is your mnclusion? O Reject Ho. We cannot conclude that there has been a significant increase In the mean domestic airfare for business travel for the oneyear periodt O Reject H0. We can conclude that there has been a signicant increase in the mean domestic airfare for business travel for the one-year periodu 0 Do not rejea H0. We cannot conclude that there has been a signicant increase in the mean domestic airfare for business navel for the one-year period. 0 Do not reject 11., We can conclude that there has been a signicant increase in the mean domestic airfare for business travel for the one-year period (b) What is the sample mean domestic airfare (in dollars) for business travel for each year? sum :3 wrsvsus s: (c) What is the percentage change in mean airfare for (he oneyear period? (Round your answer to one decimal place) \\:I% You may need to use the appropriate technology to answer this question. A standardized exam consists of three parts: math, writing, and critical reading. Sample data showing the math and writing scores for a sample of 12 students who took the exam follow. Stud-III MINI WHIIII' 1 540 474 2 432 350 3 528 463 4 574 612 5 448 414 6 502 526 7 480 430 8 499 459 s 610 609 10 572 541 11 390 335 12 593 613 (a) use a oios level of significance and test for a difference between the population mean for the math scores and the population mean for the writing scores. (Use math score writing score.) Formulate the hypotheses. Calculate the test statistic. (Round your answerto three decimal places.) |:| calculate the p-value. (Round your answer to four decimal places) p-vaiue = what is your cancluslon? O Reject Ho. We cannot conclude that there is a signicant difference between the population mean scores for the math test and the writing test. 0 Do not reject H0. We cannot conclude that there is a signicant difference between the population mean scores for the math test and the writing test. 0 Reject MD. We can conclude that there is a signicant difference between the population mean scores for the maa test and me writing test. 0 Do not reject Ha. We can conclude that there is a slgnlcanl difference between the population mean scores for the math test and the writing test (b) What is the point estimate arme difference between the mean scores for the two tests? (Use mam scare writing score.) what are the estimates of the population mean scores for the two tests? wnun E which test reports the higher mean score? The math test reports a mean score than the writing test. (b) What is the pnlnt estimate of the difference between the mean scores for the two tests? (Use math snore writing score.) E What are the estimates of the population mean scores for the two tests? Math j m. mg : which test reports the higher mean score? The math test reports a --Salecl V mean score than the writing test