Question

QUESTION 2

1. 1. A marketing researcher has to choose between three car models that consumers will want to purchase. He had 120 men and 80 women decide which of the three designs were their favorite. The results are below.

   	Car Model 1	Car Model 2	Car Model 3	Row Totals
   Men	52	28	40	120
   Women	24	26	30	80
   Column Totals	76	54	70	n = 200

   1. Assuming, a null hypothesis, how many of the women would be expected to prefer Car Model 3 and how did you come up with that number?
   2. Do the data indicate that the distribution of preference of men is significantly different from the distribution of women? Use α = 0.05 (include expected values, df, critical value, and chi-square statistic)
   3. Write out the results for part b in APA format.
   4. Name three reasons why a researcher chooses to use a nonparametric test?
   5. What is the general goal for the goodness of-fit-test compared to the general goal of the chi-square test for independence?
   6. If the above problem only looked at the men (see below), assuming a no-preference null hypothesis, how many men would be expected to prefer Car Model 2 and how did you come up with that number?

   	Car Model 1	Car Model 2	Car Model 3
   Men	52	28	40

Answer 1

a.

Women would be expected to prefer car model 3 are 28

We got the above expected value of women by this formula:-Total number of female*total number of car model 3 / total number of observation

b. d.f= (no. of rows-1)*(no. of columns-1)=2-1 * 3-1=2

alpha given is 0.05

Chi-square critical =5.991

c.

So chi-square critical value for (0.05,2)=5.991 and P-value(3.978,2)=0.1368

As P-value is greater than alpha=0.05 we fail to reject the null hypothesis.

d.Nonparametric tests are used to verify wether the data is distributed normally or not.If the data is normal then you can use parametric statistic tests.It is used when the result is ordinal variable or a rank.when there are definite outliers,or when the outcome has clear limits of detection.

e.The goodness of fit test is determined by comparing two models statistically.While the Chi-Square test of independence is used to determine if there is a significant relationship between two nominal (categorical) variables

Answer .Men who expected car model 2 are 40