Assignment 3: Problems – 8 exercises - Exercises In the exercises sections in the chapters, of your textbook, Statistics for Management and Economics, perform the following activities: "Random...

Assignment 3: Problems – 8 exercises - Exercises In the exercises sections in the chapters, of your textbook, Statistics for Management and Economics, perform the following activities: "Random Variables and Discrete Probability Distributions": 7.84 and 7.97 "Continuous Probability Distributions": 8.35 and 8.42 "Inference about Comparing two Populations": 13.5 and 13.8 "Chi-Squared Tests": 15.48 and 15.56 Submit your answers in a 4- to 5-page Microsoft Word document and import any associated work in Microsoft Excel. "Random Variables and Discrete Probability Distributions": 7.84 and 7.97: Exercise 7.84 Given a binomial random variable with n=10 and p= .3, use the formula to find the following probabilities: a) P(X = 3) b) P(X = 5) c) P(X= 8) Exercise 7.97 In the United States, voters who are neither Democrat nor Republican are called Independent. It is believed that 10% of all voters are Independent. A survey asked 25 people to identify themselves as Democrat, Republican, or Independent: a) What is the probability that none of the people are Independent? b) What is the probability that fewer than five people are independent? c) What is the probability that more than two people are Independent? "Continuous Probability Distributions": 8.35 and 8.42: Exercise 8.35 X is normally distributed with a mean of 250 and a standard deviation of 40. What value of X does only the top 15% exceed? Exercise 8.42 Travelbyus is an Internet-based travel agency wherein customers can see videos of the cities they plan to visit. The number of hits daily is a normally distributed random variable with mean of 10,000 and a standard deviation of 2,400: a) What is the probability of getting more than 12,000 hits? b) What is the probability of getting fewer than 9,000 hits? "Inference about Comparing two Populations": 13.5 and 13.8: Exercise 13.5 in 9th edition is 13.2 in the 8th edition book: In random samples of 12 from each tow normal population, we found the following statistics: 74 s1 = 18 x 2 = 71 s2 = 16 a) Test with alpha = .05to determine whether we can infer that the population means differ b) Repeat Part a increasing the standard deviation to s1 = 210 and s2 = 198. c) Describe what happens when the sample standard deviations get larger. d) Repeat Part a with samples of size 150. e) Discuss the effects of increasing the sample size. f) Repeat Part a, changing the mean of sample 1 to x1 = 76. g) Discuss the effect of increasing x1. Exercise 13.8 in the 8th edition is 13.4 in the 8th edition: Random sampling from two normal populations produced the following results: x 1 = 412 s1 = 128 n1 = 150 x2 = 405 s2 = 54 n2 = 150 a) Can we infer at the 5% significance level that is greater than ? b) Repeat Part a decreasing the standard deviations to s1 = 31 and s2 = 16. c) Describe what happens when the sample standard deviations get smaller. d) Repeat Part a with samples of size 20 e) Discuss the effects of decreasing the sample size f) Repeat Part a changing the mean of sample 1 to 409 g) Discuss the effect of decreasing 1. "Chi-Squared Tests": 15.48 and 15.56: Exercise 15.48 in the 9th edition is 15.35 in the 8th edition: A random sample of 50 observations yielded the following frequencies for the standardized intervals: Interval Frequency Z = - 1 6 -1 0 z > 1 3 Can we infer that the data are not normal? (Use alpha = .10) Exercise 15.43 in 9th edition is 15.43 in the 8th edition: Suppose that the personnel department in Exercise 15.42 continued its investigation by categorizing absentees according to the shift on which they worked, as shown in the accompanying table. Is there sufficient evidence at the 10% significance level of a relationship between the days on which employees are absent and the shift on which the employees work? Shift Monday Tuesday Wednesday Thursday Friday Day 52 28 37 31 33 Evening 35 34 34 37 41 Just in case you might need to see exercise 15.42 here it is as follows: It has been estimated that employee absenteeism costs North American companies more than $100 billion per year. As a first step in addressing the rising cost of absenteeism, the personnel department of a large corporation recorded the weekdays during which individuals in a sample of 362 absenteeism were away over the past several months. Do these data suggest that absenteeism is higher on some days of the week than on others? Day of week Monday Tuesday Wednesday Thursday Friday Number Absent 87 62 71 68 74