1. The formula for a regression equation is Y’ = 2X + 9.
a. What would be the predicted score for a person scoring 6 on X?
b. If someone’s predicted score was 14, what was this person’s score on X?
2. For the X,Y data below, compute:
a. r and determine if it is significantly different from zero.
b. the slope of the regression line and test if it differs significantly from zero.
c. the 95% confidence interval for the slope.
3. At a school pep rally, a group of sophomore students organized a free raffle for prizes. They claim that they put the names of all of the students in the school in the basket and that they randomly drew 36 names out of this basket. Of the prize winners, 6 were freshmen, 14 were sophomores, 9 were juniors, and 7 were seniors. The results do not seem that random to you. You think it is a little fishy that sophomores organized the raffle and also won the most prizes. Your school is composed of 30% freshmen, 25% sophomores, 25% juniors, and 20% seniors.
a. What are the expected frequencies of winners from each class?
b. Conduct a significance test to determine whether the winners of the prizes were distributed throughout the classes as would be expected based on the percentage of students in each group. Report your Chi Square and p values.
c. What do you conclude?
4. A geologist collects hand-specimen sized pieces of limestone from a particular area. A qualitative assessment of both texture and color is made with the following results. Is there evidence of association between color and texture for these limestones? Explain your answer.
Colour
| |||
Texture
|
Light
|
Medium
|
Dark
|
Fine
|
4
|
20
|
8
|
Medium
|
5
|
23
|
12
|
Coarse
|
21
|
23
|
4
|
5. True/False. The standard deviation of the chi-square distribution is twice the mean.
6. Do men and women select different breakfasts? The breakfasts ordered by randomly selected men and women at a popular breakfast place is shown in
Table 11.55. Conduct a test for homogeneity at a 5% level of significance.
