Question 1 For each of the following cases 1State the Hull and Alternative hypothesis 25tate if it is one or twosided 3-State if it involves one population or two 4What type of test statistics to use 1. The manager of a hotel in Duba 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 weekend guest bills to test the manager's claim. The management does not know the population standard deviation, so it will use the sample standard deviation. 2. The manager of an automobile dealership is considering a new bonus plan designed to increase sales volume. Currently, the mean sales volume B 14 automobiles per month. The manager wants to conduct a research study to see whether the new bonus plan increases sales volume. To collect data on the plan, a sample of sales personnel will be allowed to sell under the new bonus plan for a onemonth period. Develop the null and alternative hypotheses most appropriate for this research situation. The standard deviations of each of the plans are not known but assumed equal. 3. A production line operation is designed to fill cartons with laundry detergent. A sample of mrtons is periodically selected and weighed to determine whether underlling or overlilling is oocurring. The previous proportion of under or overlled cartons is 10%. The quality control engineer thinks that this proportmcreased and that the line needs adjustment. 4. I would like to compare the percentage of As in the Operations Research [0R] course to the statistim course. I think that statistics has more A percentage than OR by 10%. where the 1096 is already assumed in the department. The last on and statistics courses had 40 and 61'.) students respectively. Eight students had Ain CIR compared to 15 in statistics 5. safety training was conducted for a group of oil and gas workers. To assess the training benefits, worders knowledge before and after the training was assessed. The scores of the workers before and after the training were recorded. The training manager believes that there is no benefit for the training while the trainer thinks that the training '5 benecial. Question 2 1- A humanitarian organization helped a town in Africa dig several wells to gain access to clean water. Before the wells were in place, an average of 120 infants contracted typhoid each month. After the wells were installed, the humanitarian organization surveyed for nine months and found an average of 90 infants contracted typhoid per month. Assume that the population standard deviation is 40 and the number of infants that contract typhoid is normally distributed. a. Specify the null and alternative hypotheses to determine whether the average number of infants that contract typhoid has decreased since the wells were put in place. b. Calculate the value of the test statistic, critical value(s) and the p-value. c. At the 5% significance level, can you conclude that the number of babies falling ill due to typhoid has decreased? Use 1) critical values, 2) P-value, and 3) Confidence interval methods 2- An engineer wants to know if the average amount of energy used in his factory per day has changed since 2005. The factory used an average of 2000 megawatt hours (mwh) per day prior to 2005. Since 2005, the engineer surveyed 400 days and found the average energy use was 2040 mwh per day. Assume that the population standard deviation is 425 mwh per day. a. Specify the null and alternative hypotheses to determine whether the factory's energy use has changed. b. Calculate the value of the test statistic, critical value(s), and the p-value. c. At the 5% significance level, can you conclude that the energy usage has changed? Use 1) critical values, 2) P-value, and 3) Confidence interval methods