# Nonparametric Tests Exercises

November 20, 2016
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(This article was first published on R-exercises, and kindly contributed to R-bloggers)

In this set of exercises you will be presented with real-life problems in marketing. Your task will be to choose appropriate nonparametric statistical technique and solve the problem using appropriate R functions.

Answers to the exercises are available here.

Exercise 1

A company wants to learn if sales income is equaly distributed among the stores. In order to test it, 8 stores were randomly selected. The sales figures are: 102, 300, 102, 100, 205, 105, 71 and 92 units of product.

Are the sales equaly distributed among the stores, on the level of significance of 95%?

Exercise 2

A company sells the same product in two types of stores: classical and self-service stores. The data about income earned in each type of store are as follows:

Classical stores: 50, 50, 60, 70, 75, 80, 90, 85

Self-service: 55, 75, 80, 90, 105, 65

On the level of significance of 95%, is there a difference in income among different types of stores?

Exercise 3

Accounting data for sales showed that in randomly selected 15 stores the quantities of products sold are:

509, 517, 502, 629, 830, 911, 847, 803, 727, 853, 757, 730, 774, 718, 904

Unsatisfied with those results, a company decided to start advertising campaign. After the campaign finished, the amount of products sold in these same stores were:

517, 508, 523, 730, 821, 940, 818, 821, 842, 842, 709, 688, 787, 780, 901

Did the advertizing campaign produce statistically significant results?

Exercise 4

One product is produced in white, blue and red color. Five stores were randomly selected in order to test, with the 5% risk of error, if the color influences the number of products sold. Data about sales are given in the following table:

Store White Blue Red
1. 510 925 730
2. 720 735 745
3. 930 753 875
4. 754 685 610
5. 105

Exercise 5

A TV station conducted surveys in March, April, May and June asking a number of it’s viewers about their satisfaction with the program in the previous month. The same viewers participated in all four surveys. You can download survey data here

Did the viewer’s satisfaction change during four months?

Tip: in order to conduct this test, you’ll need to install and use `CVST` library.

Exercise 6

A company conducted survey in order to learn about customer satisfaction with company’s service. Then, after improvement of the service, company conducted another survey on the same customers. The summary of two surveys is given in the following table:

Survey Satisfied Not satisfied
Before improvement 32 68
After improvement 48 52

Is there significant change in customer’s satisfaction due to the improvement of the service?

Exercise 7

A company conducted a survey in order to examine if the frequency of usage of company’s service depends on the size of the city where it’s clients live. The summary of survey is given in the following table:

City size Frequency of service usage
Always Sometime Never
Small 151 252 603
Medium 802 603 405
Large 753 55 408

Does the frequency of usage of company’s service depend on the size of the city?

Exercise 8

A company produces product A. It expect that demand for product B to rise. In order to make production plan, it wants to obtain the data about the consumption of two products in order to find the association between them. Thus, it conducted a survey, asking 100 randomly chosen consumers about the quantities of two products they consume. The data can be downloaded here.

How strong is the association between consumption of products A and B?

Exercise 9

A company produces several models of the same product. A survey which was conducted included 200 buyers who were asked about factor that had the strongest influence on their decision to buy a product. The following data summarizes the survey:

Characteristics Male Female
Price 301 502
Design 353 155
Color 558 153

On the level of significance of 95%, is there a difference between genders in regard to characteristics of product.

Exercise 10

Using data from the previous exercise, calculate the contingency coefficient as a measure of association between gender and product characteristics.

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