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STAT20029 T2,2020 Week 10 Questions

STAT20029 (T2,2020) Questions:

Week 10

Review problem 12.4

RP12.4: The human resource manager of a large IT company collected data for days of the week on which its employees were absent from work. He randomly selects 150 of the absences which are shown in the table below. Use α = .05 to determine whether the data indicate whether absences during the various days of the week are equally likely.

Observed frequency

Mon

42

Tue

18

Wed

24

Thu

27

Fri

39

Total

150

Practice Problem 12.4

PP12.4: In one survey, female entrepreneurs were asked to select their personal definition of success from several categories. Thirty-nine per cent responded that happiness was their definition of success, 12% said sales/profit, 18% said helping others and 31% said achievements/challenge. Suppose you wanted to determine whether male entrepreneurs felt the same way and took a random sample of men, resulting in the following data. Use the chi-square goodness-of-fit test to determine whether the observed frequency distribution of data for men is the same as the distribution for women. Let α = .05.

Definition

Obs. Fre ( fo )

Happiness

42

Sales/Profit

95

Helping others

27

Achievement/Challenge

63

Total

227

Practice Problem 12.7

PP12.7: According to a recent survey, 66% of all computer companies are going to spend more on marketing this year than in previous years. Only 33% of other information technology companies and 28% of non-information technology companies are going to spend more than in previous years. Suppose a researcher wanted to conduct a survey of her own to test the claim that 28% of all non-information technology companies will spend more on marketing next year than this year. She randomly selects 270 companies and determines that 62 of the companies do plan to spend more on marketing next year. Use a= .05, the chi-square goodness-of-fit test and the sample data to determine whether the 28% figure holds for all non-information technology companies.

Review problem 12.5

RP12.5: A researcher interviewed 2067 people and asked whether they were the primary decision makers in the household when buying a new car last year. Two hundred and seven were men who had bought a new car last year. Sixty-five were women who had bought a new car last year. Eight hundred and eleven of the responses were from men who did not buy a car last year. Nine hundred and eighty-four were from women who did not buy a car last year. Use these data to determine whether gender is independent of being a major decision maker in purchasing a new car last year. Let α = .05.

Review problem 12.10

RP12.10: The following is a 3 x 2 contingency table for annual farm profit and the age of the farmer for a randomly selected sample of farmers in Fiji. Use an appropriate test to determine whether annual farm profit is related to a farmer’s age. Comment on the results of your test.

Review problem 12.6

RP12.6: Are random arrivals at a shoe store at the local mall Poisson distributed? A mall employee researched this question by gathering data for arrivals during one-minute intervals on a weekday between 6.30 pm and 8.00 pm. The data obtained follow. Use α = .05 to determine whether the observed data seem to be from a Poisson distribution. How could this result help decision making?

Activity 10.1

Activity10.1: A researcher believes that number of cars arriving at a car wash has a Poisson distribution. She collected a random sample and constructed the following frequency distribution to test her hypothesis.

She calculated that the λ = 2.24 for this data and the estimated chi-squared value is 1.92. Using α = 0.05, what is the appropriate decision for this goodness-of-fit test?

Activity 10.2

Demonstration problem 12.3

DP12-3: Consider a business statistics lecturer who is interested in knowing whether the distribution of scores in her class is normal. This information is necessary because she wants to find out what proportion of the students in the class may have special needs. Suppose the lecturer has collected data consisting of a simple random sample of 300 scores in her first-year business statistics score. A previous study determined that the average score in the course was 52.7% with a standard deviation of 15.0%. A frequency distribution of the sample scores found below. Based on the sample data, determine at the 0.01 level of significance whether the sample could have been drawn from a population in which the scores are normally distributed


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