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1. What are the mean and standard deviation of the scores in Section A?
2. We notice that Student F in Section A and Student L in Section B have the same numerical
score.
a. How do they stand relative to their own classes?
b. Which student performed better? Explain your answer.
Questions 3 through 7 involve rolling of dice.
3. Given a fair, six-sided die, what is the probability of rolling the die twice and getting a "2"
each time?
4. What is the probability of getting a "2" on the second roll when you get a "2" on the first
roll?
5. The House managed to load the die in such a way that the faces "1" and "3" show up twice as
frequently as all other faces. Meanwhile, all the other faces still show up with equal
frequency. What is the probability of getting a "6" when rolling this loaded die?
6. Write the probability distribution for this loaded die, showing each outcome and its
probability. Also plot a histogram to show the probability distribution.
7. We know that for a fair die, the most frequent sum in two rolls is seven. What is the most
frequent sum for this loaded die?
Use the data below to answer Questions 8 through 10.
A group of students from three universities were asked to pick their favorite college sport
to attend of their choice: The results, in number of students, are listed as follows:
Football Soccer Basketball
Maryland 60 20 70
Princeton 30 40 30
Duke 10 10 80
Supposed that a student is randomly selected from the group mentioned above.
8. What is the probability that the student is from Princeton or chooses football?
9. What is the probability that the student is from Duke, given that the student chooses
basketball?
10. What is the probability that the student is from Maryland and chooses soccer?
11. From a group of 7 paintings, 5 are water colors and 2 are oils. In how many ways can you
hang 3 paintings along a wall if the first and the third must be water colors but the second
one must be an oil painting?
12. Suppose that in a box of 20 iPhone devices, there are 10 with defective antennas. In a draw
without replacement, if 3 iPhone devices are picked, what is the probability that all 3 have
defective antennas?
13. The probability that an individual egg in a carton of eggs is cracked is 0.05. You have picked
out a carton of 1 dozen eggs (that’s 12 eggs) at the grocery store. Determine the probability
that at most two of the eggs in the carton are cracked.
Use the information below to answer Questions 14 and 16.
In a survey of the 3000 boy scouts in the National Capital Area Council (NCAC), it is found
that they have a mean weight of 135 lbs with a standard deviation of 15 lbs.
14. How many of the boy scouts have weights between 120 lbs and 150 lbs.?
15. What is the probability that a randomly selected boy scout weighs more than 150 lbs?
16. A Boy Scout Executive at the Head Quarter randomly selected 100 boy scouts from the
Council.
a. What is the probability that the 100 randomly selected boy scouts have a mean weight
more than 150 lbs?
b. Do you come up with the same result in Question 15? Why or why not?
Use the information below to answer Questions 17 through 20.
Given a sample size of 35, with sample mean 600 and sample standard deviation 100, we
perform the following hypothesis test.
Null Hypothesis H0 : µ = 700
Alternative Hypothesis Ha :µ ? 700
17. What is the test statistic?
18. At a 5% significance level (95% confidence level), what is the critical value in this test? Do
we reject the null hypothesis?
19. What are the border values between acceptance and rejection of this hypothesis?
20. What is the power of this test if the assumed true mean were 690 instead of 700?
Use the information below to answer Questions 21 and 22.
Below is a compilation of student distribution in our four statistics classes from the spring
of 2008.
Course Stat 200 Stat 225 Stat 230 Stat 250
Percentage 45 15 30 10
The enrollment report for spring 2010 is as follows:
Course Stat 200 Stat 225 Stat 230 Stat 250
frequency 250 70 140 50
21. What is the ? 2 test statistic for testing the claim that the enrollment in spring 2010 has the
same distribution as that in spring 2008?
22. What is the critical ? 2 value for this test at the 5% significance level (95% confidence
level)? Do the data provide sufficient evidence to conclude that 2010’s enrollment
distribution differs from the 2008 distribution? Justify your answer
Hypothesis Test versus Confidence Interval – Questions 23 through 25
Two different simple random samples are drawn from two different populations. The first
sample consists of 25 people with 10 having a common attribute. The second sample
consists of 2000 people with 1500 of them having the same common attribute.
23. Perform a hypothesis test of p1 = p2 with a 5% significance level (95% confidence level).
24. Obtain a 95% confidence interval estimate of p1 – p2.
25. Do you come up with the same conclusion for Question 23 and Question 24? Why or why
not?
Use the data in the table to answer Questions 26 through 28.
x 4 1 5 6 0
y 3 -1 5 6 2
26. Determine SSxx, SSxy, and SSyy.
27. Find the equation of the regression line. What is the predicted value when x = 4?
28. Is the correlation significant at 5% significance level (95% confidence level)? Why or why
not?
Fuel Efficiency – Questions 29 and 30
Listed below are measured MPGs from three different categories of vehicles.
Vehicle Miles per Gallon
Vehicle Category
#1 9.5 9.5 9.5 8.5 8.5
#2 8.5 7.5 7.5 8.5 8.0 8.0 7.5 7.5 7.5 7.5
#3 7.0 7.0 6.5 6.5 7.0 7.0 6.5 7.0 7.0 7.5
Calculate the mean and variance for each category
Assume the mean for all three categories is 8.00
29. What is the test statistic?
30. Use a 5% significance level (95% confidence level) to test the claim that the different vehicle
categories have the same mean MPG.
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