Problem 1: The same group of people rated both brands of coffee. Half of the subjects tasted brand A first. Half of the subjects tasted brand B first.

Subject. coffee a. coffee b

1 8 6

2 8 7

3 6 7

4 7 5

5 6 5

6 8 7

7 8 8

8 5 6

9 8 7

10 6 5

Is there a difference in the mean ratings between the two brands of coffee (use an alpha .05)?

You must use all five steps in hypothesis testing:

Restate the question as a research hypothesis and a null hypothesis about the populations.

Determine the characteristics of the comparison distribution.

Determine the cutoff sample score on the comparison distribution at which the null hypothesis should be rejected.

Determine your sample's score on the comparison distribution.

Decide whether to reject the null hypothesis.

Consider a bivariate normal posterior distribution such that Where. O, and Oz ome unknown parameters of the model, while I is the known posterior correlation between or and Question : How to use the properties of the multivariate momal distribution to get the conditional distribution below Q il Q 2 , y N N IP O z , 1 - P ) ~ PD 2 + NI - P N CO, 1 )Procter and Gambling are testing a new toothpaste. A sample of 400 individuals patticipated in the taste test and 80 indicated they like the taste. Conduct a hypothesis test to determine if at least 22% of the population will like the new toothpaste. At a 5% signicance level, use the critical value approach to determine if you should reject the null hypothesis. What is your conclusion? 0 Fail to reject H0, and conclude that more than 22% of people like the taste 0 Reject H0, and conclude that more than 22% of people like the taste O None 0 Fail to reject H0, and conclude that less than 22% of people like the taste 0 Reject H0, and conclude that less than 22% of people like the taste Procter and Gambling are testing a new toothpaste. A sample of 400 individuals participated in the taste test and 80 indicated they like the taste. Conduct a hypothesis test to determine if at least 22% of the population will like the new toothpaste. What is the null and alternative hypothesis? ONone OHO : p 0. 22 OHO : p 0. 22 OHO : p > 0. 22 and H1 : p