Question

Question 1

ASW, a regional shoe chain, has recently launched an online store. Sales via the Internet have been sluggish compared to their brick and mortar stores, and management suspects that its regular customers have concerns regarding the security of online transactions. To determine if this is the case, they plan to survey a random sample of their regular customers. Under consideration are several plans for selecting the sample. Name the sampling strategy for each.

Plan A - Regular customers belong to a rewards program and have a customer rewards ID number. Use a computer to randomly select 100 numbers.

Plan B - ASW has stores in five different cities. Randomly select one of the stores and survey all regular customers that belong to its rewards program.

Plan C - ASW has an alphabetized list of regular customers who belong to their rewards program. After randomly selecting a customer on the list, every 25th customer from that point on is chosen to be in the sample.

Plan D - Customers are grouped into four age categories (under 21, 21 to 35, 36 to 50, and older than 50).

Use a computer to randomly select a proportion of customer rewards ID numbers from each of the four age categories (in proportion with the population). Combine the samples from each of the four age groups. [4 marks]

(b) In the ASW study just described,

(i) Identify the population of interest. [2 marks]

(ii) Define the parameter. [1 mark]

(iii) What is the sampling frame? [1 mark]

(iv) How might the results be biased? [1 mark]

Question 2

(a) In each of the following, determine which of the four levels/scales of measurement (nominal,ordinal, interval, ratio) is most appropriate.
(i) Salaries of beginning insurance agents.
(ii) Survey responses of: “Strongly agree, agree, disagree, strongly disagree.”
(iii) Visa credit card numbers.
(iv) Nationalities of students in a survey.
(v) Times required to lubricate a car at a garage.
(vi) The daily ‘low temperature’ for the last month in your town.
(vii) Telephone area codes.
(viii) Consumer Reports hotel ratings of one, two, three or four stars. [8 marks]

(b) Categorize the following as either discrete qualitative, discrete quantitative or continuous quantitative.
(i) The listing of “reason given for quitting a job”.
(ii) Precise time it takes a bank teller to service a customer.
(iii) Number of damaged items in a shipment of 10,000 items.
(iv) The amount (to the nearest ounce) of antifreeze in a container.

Question 3
Following is the five-number summary of salaries (in $) for a sample of marketing managers..
(a) Would you expect the mean salary for this sample of marketing managers to be higher or
lower than the median? Explain. [2 marks]
(b) Which would be a more appropriate measure of central tendency for these data, the mean or
median? Explain. [2 marks]
(c). Calculate the range. [2 marks]
(d) Calculate the IQR. [2 marks]

Question 4

Construct the stem-and-leaf diagram for the following data:
23, 17, 26, 19, 32, 35, 43, 27, 41, 56, 63, 29, 31, 24, 70

Question 7
Use Table 1 above to calculate:
(a) the mean [3 marks]
(b) the median [4 marks]
(c) the mode [4 marks]
(d) the first quartile [4 marks]
(e) the standard deviation. [3 marks]

Answer 1

Following table represent the given data: 23 17 26 19 32 35 43 |2741 56 63 |293124 70 Stem and leaf plot for the given data: Stem-and-leaf of data N15 2 1 79 4 2 34 7 2 679 (2) 3 12 6 3 5 5 4 13 3 4 3 5 3 5 6 6 7 O Mean: Xi 23+17+26+..+24+ 70 15 536 15 - 35.73 Median Since, number of observations is 15 which is odd Hence, the middle most observation is the median for the given data. Arrange the given set of observations in an ascending or descending order Hence, the middle most observation in the given data is 31 Therefore, the median for the given data is 31 Mode: The most frequently occurred observation is known as mode Since, each and every observation occurs only once Therefore, mode is ill defined for the given data. First Quartile

Q1observation th -observati on - 4"observation Standard deviatioin 7- (23-35.73) +(17-35.73)70-35.73) -256.6381 - 16.0199 The objective is to name the sampling strategy for each plan. Plan (A): Regular customers belong to a rewards program and have a customer rewards ID number. Use a computer to randomly select 100 numbers Simple random sampling. Plan (B): ASW has stores in five different cities. Randomly select one of the stores and survey all regular customer s that belong to i ts rew ards program. Cluster sampling. Plan (C): ASW has an alphabetized list of regular customers who belong to their rewards program. After randomly selecting a customer on the list, every 25th customer from that point on is chosen to be in the sample Systematic sampling. Plan (D) Customers are grouped into four age categories (under 21, 21 to 35, 36 to 50, and older than 50) Stratified random samplin,g