The manager of the Danvers-Hilton Resort Hotel stated that the mean guest bill for a weekend is $600 or less. A member of the hotel’s accounting staff noticed that the total charges for guest bills have been increasing in recent months. The accountant will use a sample of future weekend guest bills to test the manager’s claim.a. Which form of the hypotheses should be used to test the manager’s claim? Explain.H0: μ ≥ 600 H0: μ ≤ 600 H0: μ = 600Ha: μ < 600 Ha: μ > 600 Ha: μ ≠ 600b. What conclusion is appropriate when H0 cannot be rejected?c. What conclusion is appropriate when H0 can be rejected?

You want to obtain a sample to estimate a population proportion. At this point in time, you have no reasonable estimate for the population proportion. You would like to be 95% confident that you esimate is within 0.01 of the true population proportion. How large of a sample size is required?

Note: For this problem, your answer should be rounded to two decimal places. In a particular municipality, it is believed that 25 percent of homes are not properly insulated. In order to test ?0:?=.25 vs. ??:?≠.25 (where ? is the population proportion of homes that are not properly insulated) a random sample of 300 homes was selected. In the sample, it was found that 108 homes were not properly insulated. If the null hypothesis is true, then the z-score for the sample proportion is:

You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately p = 0.8. You would like to be 97% confident that your esimate is within 2% of the true population proportion. How large of a sample size is required?

The head of a computer science department is interested in estimating the proportion of students entering the department who will choose the new computer engineering option. A preliminary sample indicates that the proportion will be around 0.35. Therefore, what size sample should the department head take if she wants to be 95% confident that the estimate is within 0.10 of the true proportion?

You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately p = 0.23. You would like to be 96% confident that your esimate is within 5% of the true population proportion. How large of a sample size is required?

Please help by providing detailed workings. Answers to a minimum of 6 d.p. Thanks

Part B and C, please.

A group of 100 people, who lived at varying distances (in kilometers) from an island nuclear power station, were asked if they thought a full evacuation of the area was required, when it went critical. The researches wanted to know if the opinion to evacuate or not depended on how far from the reactor people lived. Partial results of the questionnaire are shown in the table below. 0-3 km distance 3 -6 km distance 6 -9 km distance 9- 12 km distance Totals Evacuation needed X X X 51 Evacuation not X X XX needed Totals 28 28 23 XX XX You are doing a Chi Square test for independence. What is the expected value of the number of people living within a radius of 0-3 km who would say that evacuation was needed? XX denotes row/column totals. Give your answer to 2 decimal places.