midterm-review

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Statistics

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Jan 9, 2024

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BANA Statistics for Data Science Summer 2023/So 1 Midterm Review Questions Question 1 You are asked to conduct a survey to gauge the viability of a proposition on gun control. The survey is used to estimate the population proportion of all voters who will support this proposition. Assume that the interval estimate is conducted at the 90% confidence level. How many voters need to be polled in order to achieve a margin of error of no more than 10%? Question 2 A well-known university receives 10,000 applications from incoming students. The director of admissions monitors the mean GRE score for all applicants, and a random sample of 100 applicants were chosen from the 10,000 applications. The University estimates that the population standard deviation is equal to 60 from historic records. What is the probability that the sample mean of these 100 applicants will provide an estimate of the population mean GRE score within plus or minus 9 points of the actual population mean? Question 3 A private company that markets commemorative gold and silver coins has commissioned an artist to design a gold coin to commemorate the 2022 Winter Olympics. After a die has been made from the design, the company wants to estimate the mean weight of the coins that will be made with the die. Forty sample coins were made, and the results are given in the EXCEL spreadsheet COINS. Construct a 90% confidence interval for the mean weight of coins made with the die. Question 4 A fertilizer distributor has been selling fertilizer in 80-pound bags for several months. The Better Bureau Business has received several customer complaints that the distributor has consistently sold underweight bags, i.e., the mean weight of the bags is less than 80 pounds. To prove these complaints, the Bureau selected 36 bags from the distributor’s warehouse at random. The sample data are given in the EXCEL spreadsheet WEIGHTS. (a) Develop a hypothesis test to prove these complaints. Clearly define your notation and state the hypothesis. (b) What is the p-value of the test? (c) What is the conclusion (in layman’s terms) at 0.01 level of significance? Question 5 A credit card company is interested in comparing the performance of its two major call centers. One key quality metric is the total service times (waiting plus processing) taken by its agents to complete the service requests. A random sample of the total service times (in minutes) from the two call centers is summarized in the EXCEL spreadsheet CALL. (a) Develop a hypothesis test to show whether there is a difference in the mean total service times between the two call centers. Clearly define your notation and state the hypothesis. (b) What is the p-value of the test? (c) What is the conclusion (in layman’s terms) at 0.05 level of significance?
BANA Statistics for Data Science Summer 2023/So 2 Question 6 The Airport Authority has recently implemented a number of procedures in order to reduce the amount of flight delays at the City Airport. A departure flight is considered delayed if it is more than 15 minutes behind the scheduled departure time. The following sample data show the delayed departures at the City Airport before and after these procedures have implemented. Before Implementation After Implementation Total flight departures 900 1200 Delayed departures 252 312 (a) Develop a hypotheses test that can be used to show whether the population proportion of delayed departures has decreased after the implementation of the procedures. Clearly define your notation and state the hypotheses. (b) What is the p-value of the test? (c) What is the conclusion (in layman’s terms) at 0.05 level of significance?
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