CHI-SQUARE

CHI-SQUARE TEST  a test used in finding relation between categories.

where O = observed frequency (actual) and E = expected frequency

 degrees of freedom = (c – 1) ( r – 1)

to get E =

1.       A brand manager is concerned that her brand’s share may be unevenly distributed throughout the country.  In a survey in which the country was divided into 4 geographic regions, a random sampling of 100 consumers in each region was surveyed with the following results:

REGION

                                                NE          NW         SE           SW

Purchase the brand             40           55           45           50
do not purchase                   60           45           55           50

Calculate using .05 level of significance.

2.       To see if silicon chip sales are independent of where the U.S. economy is in the business cycle, data have been collected on the weekly sales of Zippy Chippy, an earthquake valley firm, and on whether the U.S. economy was rising to a cycle peak, at a cycle peak, falling to a cycle trough, or at cycle trough.  The results are:

WEEKLY CHIP SALES

                                                High       Medium                 Low

Economy

At peak                                  20           7                              3

At trough                               30           40                           30

Rising                                     20           8                              2

Falling                                    30           5                              5

Calculate at 0.01 level of significance.

3.       A newspaper publisher, trying to pinpoint his market’s characteristics, wondered whether newspaper readership in the community is related to readers’ educational achievement.  A survey questioned adults in the area on their level of education and their frequency of readership.  The results are shown in the following table.  Use 0.01 significance level.

LEVEL OF EDUCATIONAL ACHIEVEMENT

                                                Professional          College                   High School          Did not complete HS

Readership

Never                                     7                              14                           13                           16

Sometimes                            13                           17                           7                              7

Morning                                 39                           41                           8                              12

Both editions                        22                           23                           8                              12

4.       An educator has the opinion that the grades of high school students make are dependent on the amount of time they spend listening to music.  To test this theory, he has randomly given 400 students a questionnaire within the questionnaire are the two questions: “How many hours per week do you listen to music?” and “What is the average grade for all your classes?”  The data from the survey are in the table below.  Using a .05 percent significance level, test whether these factors are independent or dependent.

AVERAGE GRADE

                                                A                             B                             C                             D                             F

Hours spent

<5 hrs                                     13                           10                           11                           16                           5

5-10 hrs                                 20                           27                           27                           19                           2

11-20 hrs                               9                              27                           71                           16                           32

>20 hrs                                   8                              11                           41                           24                           11