Question 1

Chi Square Test for the Difference Between Two Proportions

Consider a study on the impact of using celebrities in television advertisements. A researcher investigated the relationship between gender of a viewer and the viewer's brand awareness. Three hundred TV viewers were asked to identify product advertised by male celebrities. The data were summarized in the following table.

		Gender
		Male	Female	Totals
Brand Awareness	Could Identify Product	95	41	136
	Could Not Identify Product	55	109	164
	Totals	150	150	300

1. Is there evidence of a difference between males and females in the proportion who could identify product advertised by male celebrities? Set up the null and alternative hypotheses to gain insights into the impact of using celebrities in television advertisements.
2. Conduct the hypothesis test defined in (a), using the 0.05 level of significance.
3. Conduct the hypothesis test defined in (a), using the 0.01 level of significance.
4. Are the results of the hypothesis tests different for (b) and (c)?

Question 2

Chi Square Test of Independence

A vehicle quality survey asked new owners a variety of questions about their recently purchased cars. One questions asked for the owner's rating of the vehicle using categorical responses of average, outstanding, and exceptional. Another question asked for the owner's education level with the categorical responses some high school, high school graduate, college graduate, and university graduate. Assume the sample data below are for 500 owners who had recently purchased a car.

	Education
Quality Rating	Some HS	HS Grad	College Grad	University Grad
Average	35	30	20	60
Outstanding	45	45	50	90
Exceptional	20	25	30	50

1. Compute the value ofc² for a test of independence.
2. Use a 0.05 level of significance and a test of independence to determine if a new owner's vehicle quality rating is independent of the owner's education?
3. What is the p-value and what is your conclusion?
4. Use the overall percentage of average, outstanding and exceptional ratings to comment upon how new owners rate the quality of their recently purchased cars.

Question 3

Krusskal - Wallis Test

Forty-minute workouts of one if the following activities three days a week will lead to a loss weight. The following sample data show the number of calories burned during 40-minute workouts for three different activities.

Swimming	Tennis	Cycling
408	415	385
380	485	250
425	450	295
400	420	402
427	530	268

1. At the 0.05 level of significance, is there evidence of a significant difference in the median amount of calories burned among the different activities?
2. What is your conclusion?