1. Suppose that in a large metropolitan area, 82%

1.    Suppose that in a large metropolitan area, 82% of all households have cable tv. Suppose you are interested in selecting a group of six households from this area. Let X be the number of households in a group of six households from this area that have cable tv. For what proportion of groups will at most three of the households have cable tv? 
a.    0.924
b.    0.400
c.    0.696
d.    0.304
e.    0.076
2.    A potato chip company calculated that there is a mean of 75.4 broken potato chips in each production run with a standard deviation of 5.2. If the distribution is approximately normal, find the probability that three will be fewer than 66 broken chips in a run.
a.    0.035
b.    0.335
c.    0.018
d.    0.285
e.    0.965
3.    A distribution of grades in an introductory statistics class (where A = 4, B = 3, etc) is: 
X    0    1    2    3    4
P(x)    0.09    0.19    0.21    0.32    0.19

Find the mean and variance for the grades in this class.
a.    Mean = 2.33, variance -= 1.5211
b.    Mean = 2.42, variance = 0.76055
c.    Mean = 2.33, variance = 0.76055
d.    Mean = 2.24, variance = 1.2333
e.    Mean = 2.24, variance = 1.5211
4.    The weights of male and female students in a class are summarized in the following boxplots:

 
Which of the following is NOT correct?
a.    The median median weight of the male students is about 166 pounds.
b.    About 50% of the male students have weights between 150 and 185.
c.    The mean weight of female students is about 120 because of symmetry.
d.    The male students have less variability than the female students. 
5.    Given that P(A)= 0.27, P(B) = 0.43, and P(A ∩ B) = 0.08, find P (A | B).
a.    0.844
b.    0.814
c.    0.186
d.    0.116
e.    0.296
6.    Identify the most appropriate test to use for the following situation: A private and a public university are located in the same city. For the private university, 1046 alumni were surveyed and 653 said that they attended at least one class reunion. For the public university, 791 out of 1327 sampled alumni claimed they have attended at least one class reunion. Is the difference in the sample proportions statistically significant?
a.    Two Sample Z Test For Means
b.    Two Sample z test for proportions
c.    One sample t test for mean
d.    One sample z test for mean
e.    Matched pairs t test for means
f.    One sample z test for proportions
g.    One sample t test for means
7.    A random sample of 169 cans of fruit nectar is drawn from among all cans produced in a run. Prior experience has shown that the distribution of the contents has a mean of 14.11 ounces and a standard deviation of 2.18 ounce. What is the probability that the average contents of the 169 sample cans is less than 13.74 ounces?
a.    0.973
b.    0.014
c.    0.034
d.    0.027
e.    0.986
8.    A random variable X has a probability distribution as follows:
X    0    1    2    3    4
P(X)    3k    5k    5k    3k    2k
                    

What is P(X < 2)? 
a.    1/18
b.    4/9
c.    8/9
d.    13/18
e.    Cannot be determined.
9.    Find a value of c so that P(Z ≤ c) = 0.56.
a.    -0.572
b.    -0.303
c.    1.017
d.    0.578
e.    0.151

10.    The following table displays the results of a sample of 100 in which the subjects indicated their favorite ice cream of three listed. The data are organized by favorite ice cream and age group. What is the probability that a person chosen at random will be between 20 and 40 years old if he or she favors vanilla?
Age    Chocolate    Vanilla    Strawberry
Over 40    12    7    11
20-40    15    8    12
Under 20    12    17    6

a.    ¼
b.    8/35
c.    2/25
d.    ¾
e.    23/25

11.    A random sample of 144 observations produced a sample proportion of 0.25. An approximate 90% confidence interval for the population proportion p is between
a.    0.181 and 0.319
b.    0.191 and 0.321
c.    0.214 and 0.286
d.    0.191 and 0.309
e.    0.179 and 0.321
12.    Data for gas mileage (in mpg) for different vehicles was entered into a software package and part of the ANOVA table is shown below:
Source    DF    SS    MS
Vehicle    5    505    252.50
Error    6    202    33.67
Total    11    707    

Determine the p-value for the data.
a.    0.4103
b.    0.0146
c.    0.0073
d.    0.0750
e.    0.0049

13.    If P-value is larger than the level of significance α, then the researcher should ______ at level α.
a.    Reject H0
b.    Fail to reject H0
c.    Accept H0
14.    The one-sample t statistics for a test of H0 : μ = 14 vs. Ha : μ < 14 based on n = 16 observations has the test statistic value of -1.68. What is the p-value for this test?
a.    0.057
b.    0.114
c.    0.000
d.    0.943
e.    0.357
15.    A study of iron deficiency in infants compared samples of infants whose mothers chose different ways of feeding them. One group contained breast-fed infants. The children in another group were fed a standard baby formula without any iron supplements. Here are summary results on blood hemoglobin levels at 12 months of age:
Group    n    x̅
    s
Breast-fed    27    15.3    2.2
Formula    33    16.9    1.9

Part a: We want to see if the mean hemoglobin level is greater among formula­fed babies. State the hypotheses and perform the significance test on your hypothesis. Report the test statistic and p-value. State your conclusion in terms of the issue. 

Part b: Give a 95% confidence interval for the mean difference in hemoglobin level between the two populations of infants. 

16.    Consumer Reports rated 77 cereals on a scale of 0 to 100. The number of grams of sugar contained in each serving of the corresponding cereals was also recorded. Using sugar as the explanatory variable and the Consumer Reports rating as the dependent variable, computer output of the data is as follows (the p-values are intentionally left blank):
Predictor    Coef    StDev    T    P
Constant    58.93    1.847    30.58    ---
Sugars    -2.56    0.28    -9.98    ---

S = 9.204     R-Sq = 61.2%       R-Sq(adj) = 59.9%

Part a: What is the regression equation?
Part b: Calculate the 95% confidence interval of the slope of the regression line for all cereals.
Part c: Use the information provided to test whether there is a significant relationship between the sugar content and the Consumer Report rating at the 5% level.

17.    Suppose the random variable X has CDF given by the function:
 
    Part a: Find P(X ≤ 1)
    Part b: P(0.5 ≤ X ≤ 1)
    Part c: Find the density function f(x). 

18.    Suppose you wish to test if a number cube (die) is loaded or not. If the die is not loaded, the theoretical probabilities for each roll should be:
1    2    3    4    5    6
16 2/3 %    16 2/3 %    16 2/3 %    16 2/3 %     16 2/3 %     16 2/3 %
                    

You roll the die 84 times and come up with the following distribution:
1    2    3    4    5    6
12    11    20    13    15    13

Part a: What type of test should be used in this situation?
Part b: State the hypothesis.
Part c: What is the test statistic?
Part d: Find the p-value and state your conclusion. 

19.    The following data are for intelligence-test (IT) scores, reading rates (RR), and grade-point averages (GPA) of 8 at-risk students.
IT    184    202    202    167    202    210    199    181
RR    34    30    42    34    22    45    22    25
GPA    2.4    1.8    2.9    2.3    1.8    3.1    1.7    2.0

    Part a: Calculate the line of best fit that predicts the GPA on the basis of RR scores.
    Part b: Calculate the line of best fit that predicts the GPA on the basis of IT scores.
    Part c: Which of the two lines calculated in parts a and b best fits the data? Justify your answer.