Discuss the below:
Q1. A few years ago, a cola manufacturer invited consumers to take a blind taste test. Consumers were asked to determine which of two sodas (brand 1-the manufacturer's own soda, or brand 2 -the competitor's soda) they preferred. The manufacturer was interested in determining what factors played a role in people's taste preferences. One of the factors studied was the gender of the consumer. Let p1 be the true proportion of men who prefer brand 1 and let p2 be the true proportion of women who prefer brand 1. Below is an ASP printout comparing the taste preferences of the men and women surveyed.
HYPOTHESIS: PROP. X = PROP. Y
SAMPLES SELECTED FROM soda(brand1,brand2)
males (sex=0, males) (NUMBER = 115)
females (sex=1, females) (NUMBER = 56)
X = males
Y = females
SAMPLE PROPORTION OF X = 0.422018
SAMPLE SIZE OF X = 109
SAMPLE PROPORTION OF Y = 0.25
SAMPLE SIZE OF Y = 52
PROPORTION X - PROPORTION Y = 0.172018
Z = 2.11825
Suppose the two-tailed p-value is really .0734. State the proper conclusion.
1) At alpha = .08, there is insufficient evidence to indicate the proportion of men preferring brand 1 differs from the proportion of women preferring brand 1.
2) At alpha = .05, there is sufficient evidence to indicate the proportion of men preferring brand 1 differs from the proportion of women preferring brand 1.
3) At alpha = .05, there is sufficient evidence to indicate the proportion of men preferring brand 1 equals the proportion of women preferring brand 1.
4) At alpha = .10, there is sufficient evidence to indicate the proportion of men preferring brand 1 differs from the proportion of women preferring brand 1.
Q2. A coffeehouse wishes to see if customers have any preference among 5 different brands of coffee. A sample of 200 customers provided the data below. Find the rejection region to test the claim that the probabilities show no preference. Use alpha = 0.01.
1) X^2 > 13.277
2) X^2 > 11.143
3) X^2 > 14.860
4) X^2 > 9.488
Q3. A researcher wants to determine whether the number of minutes adults spend online per day is related to gender. A random sample of 315 adults was selected and the results are shown below. Find the expected frequency for the cell E2,2 to determine if there is enough evidence to conclude that the number of minutes spent online per day is related to gender. Assuming the row and column classifications are independent, find an estimate for the expected cell count of cell E2,2.
1) 33
2) 66.9
3) 44
4) 50.1