Question 1

A manufacturer of cat food was planning to survey households in the US to determine purchasing habits of cat owners. Among the questions to be included are those that relate to

1. Where cat fat is primarily purchased.
2. Whether dry or moist cat food is purchased.
3. The number of cats living in the household.
4. Whether the cat is pedigreed.

a. Describe the population.

b. For each of the four items listed, indicate whether the variable is categorical or numerical.

Question 2

One of the major measures of the quality of service provided by any organization is the speed with which the organization responds to customer complaints. A large family-held department selling furniture and flooring, including carpet, had undergone a major expansion in the past several years. In particular, the flooring department had expanded from 2 installation crews to an installation supervisor, a measurer, and 15 installation crews. During a recent year, the company got 50 complaints concerning carpet installation. The following data represent the number of days between the receipt of the complaint and the resolution of the complaint:

54,5,35,137,31,27,152,2,123,81,74,27,11,19,126,110,110,29,61,35,94,31,26,5,12,4,165, 32,29,28,29,26,25,1,14,13,13,10,5,27,4,52,30,22,36,26,20,23,33,68

a. Construct a frequency distribution and a percentage distribution table.

b. Construct a histogram.

c. If you had to tell the president of the company how long a customer should expect to wait to have a complaint resolved, what would you say? Explain.

d. Compute the mean, median, first quartile, and third quartile.

e. Compute the range, interquartile range, variance, standard deviation.

f. Construct a box plot. Are the data skewed? If so, how?

Question 3

A survey sponsored by The American Dietetic Association and the agribusiness giant ConAgra found that 53% of office workers take 30 minutes or less for lunch each day. Approximately 37% take 30 to 60 minutes, and 10% take more than an hour.

a. What additional information you want to know before you accepted the results of the survey?

b. Discuss the four types of survey errors in the context of this survey.

Question 4

The owner of the restaurant serving Continental-style entrees was interested in studying ordering patterns of patrons for the Friday-to-Sunday weekend time period. Records were maintained that indicated the demand for dessert during the same time period. The owner decided to study two other variables, along with whether a dessert was ordered: the gender of the individual and whether a beef entre was ordered. The results are as follows:

A waiter approaches a table to make an order. What is the probability that the first customer to order at the table

a. Orders a dessert?

b. Order a dessert or a beef entre?

c. Is a female and does not order a dessert?

d. Is a female or does not order a dessert?

e. Suppose the first person that the waiter takes the dessert order from is a female. What is the probability that she does not order dessert?

f. Are gender and ordering dessert independent?

g. Is ordering a beef entre independent of whether the person orders dessert?

Question 5

According to a survey of American households, the probability that the residents own 2 cars if annual household income is over $25,000 is 80%. Of the households surveyed, 60% had incomes over $25,000 and 70% had 2 cars. Use the Bayes Theorem to calculate the probability that annual household income is at most $25,000 if the residents of a household do not own 2 cars.