stats (12Hours)

Week 3 – Homework

1. If you have samples of n1 = 12 and n2 = 15, in performing the pooled-variance t test, how many degrees of freedom do you have?

2. Assume that you have a sample of n1 = 8, with the sample mean X1 = 42, and a sample standard deviation S1 = 4, and you have an independent sample of n2 = 15 from another population with a sample mean of X2 = 34 and a sample standard deviation S2 = 5.

a. What is the value of the pooled-variance tSTAT test statistic for testing H0: µ1 = µ2?

b. In finding the critical value, how many degrees of freedom are there?

c. Using the level of significance α = 0.01, what is the critical value for a one-tail test of the hypothesis H0: µ1 ≤ µ2 against the alternative, H1: µ1 > µ2?

d. What is your statistical decision?

3. What assumptions about the two populations are necessary in Problem 2?

4. Referring to Problem 2, construct a 95% confidence interval estimate of the population mean difference between µ1 and µ2.

5. Referring to Problem 2, if n1 = 5 and n2 = 4, how many degrees of freedom do you have?

6. Referring to Problem 2, if n1 = 5 and n2 = 4, at the 0.01 level of significance, is there evidence that µ1 and µ2?

7. When people make estimates, they are influenced by anchors to their estimates. A study was conducted in which students were asked to estimate the number of calories in a cheeseburger. One group was asked to do this after thinking about a calorie-laden cheesecake. A second group was asked to do this after thinking about an organic fruit salad. The mean number of calories estimated in a cheeseburger was 780 for the group that thought about the cheesecake and 1,041 for the group that thought about the organic fruit salad. Suppose that the study was based on a sample of 20 people who thought about the cheesecake first and 20 people who thought about the organic fruit salad first, and the standard deviation of the number of calories in the cheeseburger was 128 for the people who thought about the cheesecake first and 140 for the people who thought about the organic fruit salad first.

a. State the null and alternative hypotheses if you want to determine whether the mean estimated number of calories in the cheeseburger is lower for the people who thought about the cheesecake first than for the people who thought about the organic fruit salad first.

b. In the context of this study, what is the meaning of the Type I error?

c. In the context of this study, what is the meaning of the Type II error?