Refer to the following frequency distribution for Questions 1, 2, 3, and 4.
The frequency distribution below shows the distribution for checkout time (in minutes) in MiniMart between 3:00 PM and 4:00 PM on a Friday afternoon.
Checkout Time (in minutes) | Frequency |
1.0 – 1.9 | 5 |
2.0 – 2.9 | 3 |
3.0 – 3.9 | 7 |
4.0 – 4.9 | 3 |
5.0 – 5.9 | 2 |
1. What percentage of the checkout times was less than 4 minutes? (5 pts)
1. Calculate the mean of this frequency distribution. (10 pts)
3
1. In what class interval must the median lie? (You don’t have to find the median) (5 pts)
4. Assume that the smallest observation in this dataset is 1.2 minutes. Suppose this observation were
incorrectly recorded as .2 instead of 1.2 minutes. (5 pts)
Will the mean increase, decrease, or remain the same?
Will the median increase, decrease or remain the same?
Refer to the following information for Questions 5 and 6
A 6-faced die is rolled two times. Let A be the event that the outcome of the first roll is even. Let B be the event that the outcome of the second roll is greater than 4.
5. What is the probability that the outcomes of the second roll is greater than 4, given that the first roll is an even number? (10 pts)
6. Are A and B independent? (5 pts)
Refer to the following data to answer questions 7 and 8.
A random sample of Stat 200 weekly study times in hours is as follows:
4, 14, 15, 17, 20
7. Find the standard deviation. (10 pts)
8. Are any of these study times considered unusual in the sense of our textbook? (2.5 pts)
Does this differ with your intuition? (2.5 pts)
Refer to the following situation for Questions 9, 10, and 11.
The five-number summary below shows the grade distribution of two STAT 200 quizzes.
Minimum | Q1 | Median | Q3 | Maximum | |
Quiz 1 | 12 | 40 | 60 | 95 | 100 |
Quiz 2 | 20 | 35 | 50 | 90 | 100 |
For each question, give your answer as one of the following: (a) Quiz 1; (b) Quiz 2; (c) Both quizzes have the same value requested; (d) It is impossible to tell using only the given information. (5 pts each)
9. Which quiz has less interquartile range in grade distribution?
10. Which quiz has the greater percentage of students with grades 90 and over?
11. Which quiz has a greater percentage of students with grades less than 60?
12. What is the probability that a randomly selected senior is in at least one of the two classes?
(10 pts)
13. If the student is in the Calculus class, what is the probability the student is also in the Statistics class? (10 pts)
14. A random sample of 225 SAT scores has a mean of 1500. Assume that SAT scores have a population
standard deviation of 300. Construct a 95% confidence interval estimate of the mean SAT scores.
(15 pts)
Refer to the following information for Questions 15, 16, and 17.
A box contains 5 chips. The chips are numbered 1 through 5. Otherwise, the chips are identical. From this box, we draw one chip at random, and record its value. We then put the chip back in the box. We repeat this process two more times, making three draws in all from this box.
15. How many elements are in the sample space of this experiment? (5 pts)
16. What is the probability that the three numbers drawn are all different? (10 pts)
17. What is the probability that the three numbers drawn are all odd numbers? (10 pts)
Questions 18 and 19 involve the random variable x with probability distribution given below.
X | 2 | 3 | 4 | 5 | 6 |
P(x) | 0.1 | 0.2 | 0.4 | 0.1 | 0.2 |
18. Determine the expected value of x. (10 pts)
19. Determine the standard deviation of x. (10 pts)
Consider the following situation for Questions 20 and 21.
Mimi just started her tennis class three weeks ago. On Average, she is able to return 15% of her opponent’s serves. If her opponent serves 10 times, please answer the following questions.
20. Find the probability that she returns at most 2 of the 10 serves from her opponent. (10 pts)
21. How many serves is she expected to return? (5 pts)
22. Given a sample size of 64, with sample mean 730 and sample standard deviation 80, we perform
the following hypothesis test. (20 pts)
Ho ? = 750
H1 ? < 750
What is the appropriate distribution for performing this Hypothesis test?
Z distribution, t distribution, Chi Square distribution, Empirical Rule
What is the critical value of the test statistic at ?= 0.05 level?
What is the P-value for this Hypothesis Test?
What is your conclusion (decision) for this hypothesis test at ?= 0.05 level?
Refer to the following information for Questions 23, 24, and 25.
The heights of pecan trees are normally distributed with a mean of 10 feet and a standard deviation of 2 feet.
23. What is the probability that a randomly selected pecan tree is between 10 and 12 feet tall? (10 pts)
24. Find the 3^{rd} quartile of the pecan tree distribution. (5 pts)
25. If a random sample of 100 pecan trees is selected, what is the standard deviation of the sample mean? (5 pts)
26. Consider the hypothesis test given by
Ho ? = 530
H1 ? ? 530
In a random sample of 81 subjects, the sample mean is found to be 524. Also, the population standard deviation is ?= 27. (20 pts)
Calculate the Test Statistic.
Is there sufficient evidence to justify the rejection of Ho at ?= 0.01 level?
27. A certain researcher thinks that the proportion of women who say that the earth is getting warmer
is greater than the proportion of men. (25 pts)
In a random sample of 250 women, 70% said that the earth is getting warmer.
In a random sample of 220 men, 68.18% said that the earth is getting warmer.
At the .05 significance level, is there sufficient evidence to support the claim that the proportion of
women saying the earth is getting warmer is higher than the proportion of men saying the earth is
getting warmer?
What is the Null Hypothesis?
28. Find an equation of the least squares regression line. (15 pts)
Complete the following table:
x | y | x^2 | xy | y^2 |
0 | 4 | 0 | 0 | 16 |
-1 | -2 | 1 | 2 | 4 |
1 | 5 | 1 | 5 | 25 |
2 | 6 | 4 | 12 | 36 |
3 | 8 | 9 | 24 | 64 |
5 | 21 | 15 | 43 | 145 |
What is the Y intercept of the equation?
29 Using the equation you calculated in question 28 What is the predicted value of y if x=4? (10 pts)
30. The Daily News reported that the color distribution for plain M&M’s was: 40% brown, 20% yellow, 20% orange, 10% green, and 10% tan. Each piece of candy in a random sample of 100 plain M&M’s was classified according to color, and the results are listed below. Use a 0.05 significance level to test the claim that the published color distribution is correct. (25 pts)
Color | Brown | Yellow | Orange | Green | Tan |
Number | 45 | 13 | 17 | 7 | 18 |
What is the Null Hypothesis?
What is the degrees of freedom for this Hypothesis test?
What is the numerical Chi Square critical value?
What is the numerical value of the Chi Square test statistic?
31. Please note: Each time you re-due the Final Exam the answer to question 31 may change, but the subject matter and format will not change.