Question;Show all your work and formulae.All hypothesis tests MUST use the five steps. Formulae are necessary inall cases. The conclusions MUST be complete and include the two parts.1. (6) An office receives 20 faxed orders every two hours.a. (2) What is the probability that it will receive 8 orders in the next hour?b. (2) What is the probability that an order will be faxed within the next 9 minutes?c. (2) What is the probability that more than 12 minutes will elapse between faxed orders?2. (13) The student body of a local college draws 40% of its students from Ontario, 35%from the rest of Canada, and the remainder from outside Canada. Of those from Ontario,60% are female, of those from the rest of Canada 25% are female, and of those fromoutside Canada, 15% are female.a. (3) What is the probability of a male student from Ontario?b. (5) What is the probability of a female student?c. (5) What is the probability of a male student who did not come from Ontario?3. (19) The number of cups of coffee served at a local Tim Horton?s during the morningrush hour between 7 and 9 AM is normally distributed. Less than 200 cups served isconsidered a slow day, 200- 249 an average day, and over 250 a busy day. A randomsample of five days was taken and the sales figures observed. The results are as follows:184212194250200a. (5) Calculate the sample average and sample standard deviation for this data.b. (5) Construct a 99% confidence interval for the population average sales for this period.c. (2) Based on your confidence interval, can you conclude the type of day that the averagesales would be considered as defining ? slow, average, or busy? Explain your conclusion.d. (6) Management is concerned that the average is falling below the national average of 210cups during this period. Test this hypothesis using alpha = 0.05.e. (1) What assumptions must hold to allow you to construct the confidence interval and testthe hypothesis in this case?4. (18) The life insurance industry maintains that the average worker in Saskatoon has nomore than $25,000 of personal life insurance. You believe it is higher. You sample 100workers in Saskatoon at random and find the sample average to be $26,650 of personallife insurance. The population standard deviation is known to be $12,000. Use?=0.05throughout.a. (6) Test your belief using a significance level of 5%.b. (6) Explain, in the context of this question, what is meant by a Type I error, a Type IIerror, and the power of the test?c. (5) If the true average for this population is in fact $30,000, what is the probability ofcommitting a Type II error?d. (1) Calculate the power of the test.5. (24) Shoplifting costs retail businesses a great deal of money every year. In spite of thisthe historical evidence suggests that only 50% of all shoplifters are turned over to thepolice. A random survey of 40 retailers revealed that 24 of them had turned their mostrecent shoplifter in to the police. Use alpha = 0.05 for all tests.a. (6) Test to see if this sample data indicates that more shoplifters are being turned in thanin the past?b. (2) What assumptions must hold for this test to be performed?c. (2) Find the p-value for part a. (It is the probability that z is greater than the absolutevalue of the test statistic in part a.)d. (2) Describe both Type I and Type II errors in the context of this problem.e. (5) Calculate the probability of Type II error if the true proportion of shoplifters turnedover to police is 55%.f. (5) Calculate the probability of Type II error if the true proportion of shoplifters turnedover to police is 55%, if the sample size is increased to 100.g. (2) What does this tell you about the relationship between alpha, beta and sample size?
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