Elementary Statistics Out of region Test 2 Probability distributions, Central Limit Theorem, Hypothesis Testing and Confidence Intervals Due: This test is due Friday, August 5th , 8:02 am. Your signature here indicates that you did not ask for assistance on these problems from any human being who is not in our class. Please use Excel appropriately and write detailed explanations of computations, results, and conclusions. Drawing diagrams will increase the likelihood of earning more points of partial credit. Please recall that you should submit one file- if you are submitting pictures of had written work, the pictures should be embedded in a Word or pdf file for submission. Return this signature page indicating your adherence to the rules with your solutions. Signed____________________________________________ 1. A search engine site claims that, on average, one out of five visitors clicks on an ad. (a) If 12 users visit the site, what is the probability that at least one clicks on an ad? (b) If 12 users visit the site, what is the probability that more than three of them click on an ad? (c) If 1200 users visit the site, would the probability that more than 300 click on an ad be higher or lower than the answer found in part (b)? Write a few sentences explaining your answer- computations are not required (or desired) (d) Suppose 90 users visit the site during a particular minute, use the normal approximation to estimate the probability that less than 20 of them click on an ad. (e) If 900 users visited the site, would the probability that less than 200 of them click on an ad be higher or lower than the answer found in part (d)? Write a few sentences explaining your answer- computations are not required (or desired) 2. Suppose the weight of eggs produced by Henly Farms has a normal distribution with a mean of 59.4 grams and a standard deviation of 3.7 g. Find the probability that a carton of a dozen eggs will weigh less than 728 g. 3. A health insurance company charges policyholders a $2100 annual premium for health insurance for hospitalization. The company estimates that each time a patient is hospitalized costs the company $1750. Furthermore, they have estimated that 85% of patients will not be hospitalized, 10% will be hospitalized once a year, and no one will be hospitalized more than twice. (a) Find the insurance company's expected profit per policyholder. (b) What is the expected profit if they enroll 80,000 policyholders? 4. The College Board publishes the results of an achievement test stating that the average score is 1024 with a standard deviation of 178 points. A test preparation school coached 43 students for the exam. Their students had an average score of 1094. Test if the coached students scored higher than the average using = 0.03 and the prob-value approach. 5. The IRS claims that it takes 87.3 minutes to prepare a tax form. You believe it takes longer than 87.3 minutes. You survey 25 people and find the following preparation times: 56, 57, 63, 65, 70, 76, 79, 84, 85, 88, 90, 94, 95, 95, 98, 98, 101, 90, 100, 110, 111, 115, 123, 137, 142 Determine if the preparation time is significantly longer than 87.3 minutes. Use = .025. 6. Given below are the birth weights of babies born to mothers who took special vitamin supplements while pregnant: 3.13 4.37 3.93 4.33 3.39 3.68 4.68 3.52 3.02 4.29 2.47 4.13 4.47 3.22 3.43 2.54 a. Make a 95% confidence interval for the mean weight of babies whose mothers take vitamin supplements. b. Do a hypothesis test to determine if these babies weight is more than the mean weight for the population of all babies which is 3.39 kg using = .025 c. In a short paragraph, describe the relationship between your answer to part (a) and your answer to part (b). 7. A researcher studying air quality found the following levels of ozone particles (parts per million) at 20 test sites: 13 17 18 15 22 20 16 20 12 18 21 14 18 23 17 17 19 20 16 18 a. Make a 99% confidence interval for the mean ozone level in the entire city. b. Do a hypothesis test to determine if the ozone level in the city is more than the national standard for ozone which is 16.9 parts per million using = .005 8. The national standard for salinity (salt content) in drinking water is 500 parts per million. A government inspector tests the drinking water at 10 locations around a certain city and finds the following levels of salinity (in parts per million of course): 532 560 506 452 425 531 582 376 529 629 (a) Make a 95% confidence interval for the mean salinity level in this city. (b) Is this city's salinity level above the national standard? (Use = 0.025 and the result from part (a)) c. In a short paragraph, describe the relationship between your answer to part (a) and your answer to part (b)