Random samples of 47 male students and 53 female students at the U of A were asked to state their car preference (American, European, and Japanese). The resulting frequencies are shown in the following table. Is there enough evidence to conclude a difference in car preference between males and females?

American European Japanese

Male 16 10 21

Female 10 23 20

(a) In performing this statistical test, state the hypotheses.

H0: the distribution of preference is not the same for males and females vs. HA: the distribution of preference is the same for males and females

H0: the proportion of males is the same for each car preference vs. HA: the proportion of males is not the same for each car preference

H0: the distribution of gender is not the same for each car preference vs. HA: the distribution of gender is the same for each car preference

H0: the distribution of preference is the same for males and females vs. HA: the distribution of preference is not the same for males and females

H0: the proportion of females is the same for each car preference vs. HA: the proportion of females is not the same for each car preference

(b) What is the expected frequencies of each cell?Fill out the table. (Round your answers to 2 decimal places, if needed.)

American European Japanese

Male 12.22

Female 21.73

(c) What is the test statistic value for this hypothesis test? (Round your answers to 2 decimal places, if needed.)

TS=

(d) The test statistic follows a

a. chi-square distribution with df = 98

b. chi-square distribution with df = 2

c.t-distribution with df = 6

d.chi-square distribution with df = 6

e. t-distribution with df = 2

.

(e) Using the statistical table, the p-value is

a. 0.01 < p-value < 0.025

b.0.05 < p-value < 0.10

c.0.025 < p-value < 0.05

d.p-value > 0.10

e.0 < p-value < 0.005

f. 0.005 < p-value < 0.01

.

(f) Based on the p-value, those conducting the test should(?) a. reject b. fail to reject the null hypothesis at the significance level of 0.05.

(g) What is the appropriate conclusion?

There is insufficient evidence to conclude there is a difference in males and females for car preference.

There is insufficient evidence to conclude the proportion of males is not the same for each car preference.

There is sufficient evidence to conclude there is a difference in males and females for car preference.

There is sufficient evidence to conclude the proportion of males is not the same for each car preference.

There is sufficient evidence to conclude there is no difference in males and females for car preference.