1 QBA201 Quantitative Business Analysis Homework Assignment 4 Spring 2016 Instructions: The due date for this homework assignment is on Thursday, May 12th. No assignments will be accepted after the end of class and any assignments not received by the end of class will receive a grade of 0. You may use Microsoft Word, Excel, or a combination of the two to type and print out your answers. If you submit handwritten answers, make sure that your submission is neat, legible and professional in appearance. If you use multiple pages, please staple the pages together (no folders or binders, please). Finally, place a header on the paper that includes your name, ID and section number (Section 1,2 or 3) and show your work for all questions to receive full credit. 1. (10 points) The assembly line that produces an electronic component of a missile system has historically resulted in a 3% defective rate. A random sample of 500 components is drawn. What is the probability that the defective rate is greater than 5%? Suppose that in the random sample the defective rate is 5%. Explain what the result you found suggests about the defective rate on the assembly line? 2. (10 points) A business student claims that, on average, business students have to take more classes than students in other colleges. She claims that business students take more than 4 classes per semester. To examine this claim, a statistics professor asks a random sample of 10 business students to report the number of classes that they take. The results are exhibited below. Can the professor conclude, at the 5% level of significance, that the claim is true? Assume that the number of classes is normally distributed with a standard deviation of 1.5. 3 6 4 5 5 6 4 3 4 5 a. State the null and alternative hypotheses. b. Test the student's claim by calculating the p-value. Show all intermediate steps. c. How do you know whether the student's claim is supported or not? 3. (10 points) A federal agency responsible for enforcing laws governing weights and measures routinely inspects packages to determine whether the weight of the contents is at least as great as that advertised on the package. A random sample of 18 containers whose packaging states that the contents weigh 8 ounces was drawn. The contents were weighed and the results follow. a. Can we conclude at the 5% significance level that on average the containers are mislabeled? b. How do you know? Explain. 7.8 7.91 7.93 7.99 7.94 7.75 7.97 7.95 7.79 8.06 7.82 7.89 7.92 7.87 7.92 7.98 8.05 7.91 4. (10 points) Several students and faculty at AUS make international calls during the academic year. A survey of 12 students and faculty revealed the following information about the number of times an international call is made during the spring semester. Assume that the number of calls made is normally distributed with a standard deviation of 12 calls. a. Estimate with 90% confidence the average number of calls during the spring semester. b. How large a sample should we take so that the mean number of calls is within 2 calls with 95% confidence? 3 41 17 1 33 37 18 15 17 12 29 51 2 5. (10 points) A fast-food company is considering building a restaurant at a certain location. Based on financial analyses, a site is acceptable only if the number of pedestrians passing the location averages more than 100 per hour. The number of pedestrians observed for each of 40 different one-hour periods. The number of pedestrians was then recorded to be 105.7. Assume that the population standard deviation is known to be 16. a. State the null and alternative hypotheses. b. Can we conclude at the 5% significance level that the site is acceptable? How do you know? c. Please state which type of error (Type I or Type II) may be committed here? Consider your conclusion in part (b) of this question and explain your answer. Also, what are the implications of committing such error? 6. (10 points) A fitness trainer wants to estimate the average weight loss of people who are in his new workout class. In a preliminary study, he guesses that the standard deviation of the population of weight losses is about 10 pounds. a. How large of a sample should he take to estimate the mean weight loss to within two pounds, with 99% confidence? b. How large of a sample should he take to estimate the mean weight loss to within two pounds, with 95% confidence? 7. (10 points) A statistics practitioner is in the process of testing to determine whether there is enough evidence to infer that the population mean is different from 180. She calculated the mean and standard deviation of a sample of 200 observations as 𝑋 ̅ = 175 and s = 22. a. Calculate the value of the test statistic (you must decide whether the z or t is appropriate) to determine whether there is enough evidence at the 5% significance level. b. Repeat this with s = 45. c. Discuss what happens to the test statistic when the standard deviation increases. 8. (10 points) A chain coffee shop owner buys a new espresso machine and wants to determine whether this new machine is generating any profits. To test the profitability of the machine, the owner collects data on the profit made (in thousands of dollars) from 16 randomly selected stores and finds that the sample mean and sample standard deviation are $500 and $200, respectively. If the profit level is normally distributed a. State the null and alternative hypothesis. b. Test the hypotheses using a standardized test statistic at 5% significance level. c. Explain the results you find. 9. (10 points) A politician claims that the average UAE resident is more than 20 pounds overweight. To test his claim, a random sample of 20 UAE residents was weighed, and the difference between their actual and ideal weights was calculated. The data are listed below. Do these data allow us to infer at the 5% significance level that the politician's claim is true? 10. (10 points) Has the building and allocating Terminal 3 to Emirates Airlines resulted in better on-time performance? Before terminal 3 was built and allocated to Emirates Airlines, Emirates airline claimed that 92% of its flights were on time. A random sample of 165 flights completed this year reveals that 153 were on time. Can we conclude at the 5% significance level that the Emirates airline's on-time performance has improved after allocating terminal 3 only to Emirates airline? 16 23 18 41 22 18 23 19 22 15 18 35 16 15 17 19 23 15 16 26