A randomly selected sample of 500 autombile owners were ques

A randomly selected sample of 500 autombile owners were questioned on the main reason they had purchased their current automobile. The results are given below. Suppose you are asked to conduct a statistical test to determine whether or not the main reason to purchase a car in independed of gender.

styling engineering fuel economy total

Male 70 130 150 350

female 30 20 100 150

total 100 150 250 500

A. state null and alternative hypotheses

b. waht is the appropriate statistical test to use

c. use 5% level of significance to test the hypothesis.

d. what is the value of the test statistic

e. what is the p value associated with the test statistic

f. reject or not reject?

Solution

Ans: A. Hypothses

H₀: Purchase a car is independent among the gender.
H_a: Purchase a car is not independed among gender.

B. The appropriate statistical test is Chi-Square Test for Independence.

C and D. X² =Sum((Observed-Expected)^2)/Expected

The calculated X² value (valueis 31.746. The table value of X² for 0.05 level of significance with 4 degree of freedom is 9.49. The table value (9.49) is less than calculated value (31.746). Therefore, we can not accept the null hypothesis. Hence, we conclude that there is a relationship between gender and purchase a car (purchase a car is dependent among the gender.

E. The associated p-value is  P(² > 31.746) =0.0000

F. Since the P-value (0.0000) is less than the significance level (0.05), we cannot accept the null hypothesis. Thus, we conclude that there is a relationship between gender and purchase a car.