Question 1. Conduct a goodness-of-fit test to determine if the actual college majors of graduating males fit the distribution of their
expected majors.
|
Major
|
Men - Expected Major
|
Men - Actual Major
|
|
Arts & Humanities
|
11.0%
|
600
|
|
Biological Sciences
|
6.7%
|
330
|
|
Business
|
22.7%
|
1130
|
|
Education
|
5.8%
|
305
|
|
Engineering
|
15.6%
|
800
|
|
Physical Sciences
|
3.6%
|
175
|
|
Professional
|
9.3%
|
460
|
|
Social Sciences
|
7.6%
|
370
|
|
Technical
|
1.8%
|
90
|
|
Other
|
8.2%
|
400
|
|
Undecided
|
6.6%
|
340
|
Table 1
Question 2. Do men and women select different breakfasts? The breakfasts ordered by randomly selected men and women at apopular breakfast place is shown in Table 2. Conduct a test for homogeneity at a 5% level of significance.
|
|
French Toast
|
Pancakes
|
Waffles
|
Omelettes
|
|
Men
|
47
|
35
|
28
|
53
|
|
Women
|
65
|
59
|
55
|
60
|
Table 2
Question 3. Test of a Single Variance
Suppose an airline claims that its flights are consistentlyon 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 next25 flights. The average delay for those 25 flights is 22 minutes with a standard deviation of 15 minutes.
a Is the traveler disputing the claim about the average or about the variance?
b. Is this a right-tailed, left-tailed, or two-tailed test?
c. df= ________
d. p-value = ________
f. Let α = 0.05
Decision: ________
Conclusion (write out in a complete sentence.): ________
Question 4.
The cost of a leading liquid laundry detergent in differentsizes is given in Table 3.
|
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: y = 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? Whyor why not?
j. What is the slope of the least-squares (best-fit) line? Interpret the slope.