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 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.
14. A geologist collects handspecimen 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 limestones? Explain your answer.

Colour 

Texture 
Light 
Medium 
Dark 
Fine 
4 
20 
8 
Medium 
5 
23 
12 
Coarse 
21 
23 
4 
102. 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.

French Toast 
Pancakes 
Waffles 
Omelettes 
Men 
47 
35 
28 
53 
Women 
65 
59 
55 
60 
Use the following information to answer the next two exercises. The cost of a leading liquid laundry detergent in different sizes is given in Table 12.31.
Size (ounces) 
Cost ($) 
Cost per ounce 
16 
3.99 

32 
4.99 

64 
5.99 

200 
10.99 

Table 12.31
82.
a.Using “size” as the independent variable and “cost per ounce” as the dependent variable, draw a scatter plot of the data.
b.Does it appear from inspection that there is a relationship between the variables? Why or why not?
c.Calculate the leastsquares line. Put the equation in the form of: ŷ = a + bx
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 leastsquares line. Put the equation in the form of: ŷ = a + bx
d.Find the correlation coefficient. Is it significant?
e.If the laundry detergent were sold in a 40ounce size, find the estimated cost.
f.If the laundry detergent were sold in a 90ounce 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 leastsquares line valid for predicting what a 300ounce size of the laundry detergent would you cost? Why or why not?
We states our hypotheses as
H0: The fit is good.
H1: The fit is not good.
Level of significance: α = 0.05(5%)
Critical region:
Χ2 > Χ20.05 and Χ2 < Χ20.95 for v = (r1) (c1) degree of freedom.
Test statistics:
Χ2 = ∑▒(E0)^2/E
The expected frequencies are cal...