Question

Question: Shopping on Black Friday. Refer to the International Journal of Retail and Distribution Management (Vol. 39, 2011) survey of Black Friday shoppers, Exercise 6.16 (p. 340). One question was, “How many hours do you usually spend shopping on Black Friday?”

a. How many Black Friday shoppers should be included in a sample designed to estimate the average number of hours spent shopping on Black Friday if you want the estimate to deviate no more than 0.5 hours from the true mean?

b. Devise a sampling plan for collecting the data that will likely result in a representative sample.

Short answer

a. The Black Friday shoppers should be included in a sampledesigned to estimate the average number of hours spent shopping on Black Friday is 117.

b. The required sampling plan is, to select various stores from various locations. Then choose the shoppers from the stores and then collect the data from the selected shoppers.

Step-by-step solution

Given Information

The required data set mentioned in Exercise 6.16 is,

Compute the standard deviation

The standard deviation can be calculated b

Compute the value

Let the confidence level be 0.95

(a) Compute the sample size

The formula used for obtaining the sample size is,

Where SE is the sampling error, here the sampling error is 0.5 hours.

The value of is usually unknown. It can be estimated by the standard deviation, s from the prior sample

The sample size is calculated as

Hence, the Black Friday shoppers should be included in a sampledesigned to estimate the average number of hours spent shopping on Black Friday is 117.

5: (b) State the sampling plan.

The sampling plan for collecting the data results in a representative of the entire sample will vary. One such plan is given below:

First, select various stores from a variety of locations. Then choose the shoppers from the stores and collect the data from the selected shoppers.

This sample would result in a representative of the entire population.