STAT 200 homework 7

HW Assignment #7

Problem 1: Lane

2. The formula for a regression equation is 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?

Problem 2: Lane

6. 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.

X	Y
4	6
3	7
5	12
11	17
10	9
14	21

The linear regression line for this set of data is:

Problem 3:

5. 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?

Expected Frequency for freshmen = 0.3*36 =

Expected Frequency for sophomores = 0.25* 36 =

Expected Frequency for juniors = 0.25*36 =

Expected Frequency for seniors = 0.2*36 =

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?

Problem 5: Illowski

70. The standard deviation of the chi-square distribution is twice the mean.

Problem 6: Illowski

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. Conduct a test for homogeneity at a 5% level of significance.

Problem 7 and 8:

11.6 Test of a Single Variance

Use the following information to answer the next twelve exercises: Suppose an airline claims that its flights are consistently on time with an average delay of at most 15 minutes. It claims that the average delay is so consistent that the variance is no more than 150 minutes. Doubting the consistency part of the claim, a disgruntled traveler calculates the delays for his next 25 flights. The average delay for those 25 flights is 22 minutes with a standard deviation of 15 minutes.

113. DF = 25 -1 =

117. Let ? = 0.05

Decision: _

Conclusion (write out in a complete sentence.): ____

Problem 9:

66. Can a coefficient of determination be negative? Why or why not?

The coefficient of determination r2, is equal to the square of the correlation coefficient. It can never be negative as it represents the percent of variation in the dependent variable y that can be explained by variation in the independent variable x using the regression line.

Problem 10:

82.

Size (ounces)	Cost ($)	Cost per ounce
16	3.99
32	4.99
64	5.99
200	10.99

a. Using “size” as the independent variable and “cost” as the dependent variable, draw a scatter plot.

b. Does it appear from inspection that there is a relationship between the variables? Why or why not?

c. Calculate the least-squares line. Put the equation in the form of: ? = a + bx

d. Find the correlation coefficient. Is it significant?

e. If the laundry detergent were sold in a 40-ounce size, find the estimated cost.

f. If the laundry detergent were sold in a 90-ounce size, find the estimated cost.

g. Does it appear that a line is the best way to fit the data? Why or why not?

h. Are there any outliers in the given data?

i. Is the least-squares line valid for predicting what a 300-ounce size of the laundry detergent would you cost? Why or why not?

j. What is the slope of the least-squares (best-fit) line? Interpret the slope.