Solving 30 Questions on Descriptive Statistics

Answer all 30 questions. Make sure your answers are as complete as possible. Show all of your work and reasoning. In particular, when there are calculations involved, you must show how you come up with your answers with critical work and/or necessary tables. Answers that come straight from programs or software packages will not be accepted.

Refer to the following table for Questions 1, 2, and 3. Show all work. Just the answer, without supporting work, will receive no credit.

The table shows temperatures on the first 12 days of October in a small town in Maryland.

Date Temperature Date Temperature Date Temperature
Oct 1 73 Oct 5 53 Oct 9 66
Oct 2 65 Oct 6 52 Oct 10 75
Oct 3 65 Oct 7 62 Oct 11 52
Oct 4 70 Oct 8 55 Oct 12 57

1. Determine the five-number summary for this data. (10 pts)
2. Determine the mean temperature. (3 pts)
3. Determine the mode(s), if any. (2 pts)

Refer to the following frequency distribution for Questions 4, 5, 6, and 7. Show all work. Just the answer, without supporting work, will receive no credit.

The frequency distribution below shows the distribution for checkout time (in minutes) in UMUC MiniMart between 3:00 and 4:00 PM on a Friday afternoon.

Checkout Time (in minutes) Frequency
1.0 - 1.9 6
2.0 - 2.9 7
3.0 - 3.9 2
4.0 - 4.9 3
5.0 - 5.9 2
4. What percentage of the checkout times was less than 5 minutes? (5 pts)
5. Calculate the mean of this frequency distribution. (5 pts)

6. Calculate the standard deviation of this frequency distribution. (10 pts)
7. Assume that the smallest observation in this dataset is 1.2 minutes. Suppose this

observation were incorrectly recorded as 0.12 instead of 1.2. Will the mean increase, decrease, or remain the same? Will the median increase, decrease or remain the same? Explain your answers. (5 pts)

Refer to the following information for Questions 8 and 9. Show all work. Just the answer, without supporting work, will receive no credit.

A 6-faced die is rolled two times. Let A be the event that the outcome of the first roll is greater than 4. Let B be the event that the outcome of second roll is an odd number.

8. What is the probability that the outcome of the second roll is an odd number, given that the first
roll is greater than 4? (10 pts)
9. Are A and B independent? Why or why not? (5 pts)

Refer to the following data to answer questions 10 and 11. Show all work. Just the answer, without supporting work, will receive no credit.

A random sample of STAT200 weekly study times in hours is as follows:

2 14 15 18 20

10. Find the standard deviation. (10 pts)
11. Are any of these study times considered unusual in the sense of our textbook? Explain.

Does this differ with your intuition? Explain. (5 pts)

Refer to the following information for Questions 12 and 13. Show all work. Just the answer, without supporting work, will receive no credit.

There are 1500 juniors in a college. Among the 1500 juniors, 200 students are taking STAT200, and 100 students are taking PSYC300. There are 50 students taking both courses.

12. What is the probability that a randomly selected junior is in at least one of the two

courses? (10 pts)
13. What is the probability that a randomly selected junior takes only one course? (10 pts)

Refer to the following information for Questions 14, and 15. Show all work. Just the answer, without supporting work, will receive no credit.

A box contains 10 chips. The chips are numbered 1 through 10. 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.

14. How many elements are in the sample space of this experiment? (5 pts)
15. What is the probability that the three numbers drawn are all multiples of 3? (10 pts)

Questions 16 and 17 involve the random variable x with probability distribution given below.

Show all work. Just the answer, without supporting work, will receive no credit.

x 1 2 3 4 5
P ( x) 0.1 0.2 0.3 0.1 0.3

16. Determine the expected value of x. (10 pts)
17. Determine the standard deviation of x. (10 pts)

Consider the following situation for Questions 18, 19 and 20. Show all work. Just the answer, without supporting work, will receive no credit.

Mimi just started her tennis class three weeks ago. On average, she is able to return 35% of her opponent's serves. Let random number X be the number of serves Mimi returns. As we know, the distribution of X is a binomial probability distribution. If her opponent serves 10 times, please answer the following questions:

18. What is the number of trials (n), probability of successes (p) and probability of failures (q),
respectively? (5 pts)
19. Find the probability that she returns at least 2 of the 10 serves from her opponent . (10 pts)
20. Find the mean and standard deviation for the probability distribution. (10 pts)

Refer to the following information for Questions 21, 22, and 23. Show all work. Just the answer, without supporting work, will receive no credit.

The heights of pecan trees are normally distributed with a mean of 10 feet and a standard deviation of 2 feet.

21. What is the probability that a randomly selected pecan is between 8 and 12 feet tall? (10 pts)
22. Find the 80th percentile of the pecan tree height distribution. (5 pts)
23. If a random sample of 64 pecan trees is selected, what is the standard deviation of the sample

mean? (5 pts)

24. A random sample of 625 SAT scores has a mean of 1500. Assume that SAT scores have a population standard deviation of 250. Construct a 95% confidence interval estimate of the mean SAT scores. Show all work. Just the answer, without supporting work, will receive no credit.

(15 pts)

  25 .

25. Given a sample size of 81, with sample mean 730 and sample standard deviation 90, we perform the following hypothesis test at the   0.05 level.

H0 :   750

H1 :   750

(a) Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit.

(b) Determine the critical value. Show all work; writing the correct critical value, without supporting work, will receive no credit.

(c) What is your conclusion of the test? Please explain. (20 pts)

26. Consider the hypothesis test given by H0 :   530

H1 :   530.

In a random sample of 225 subjects, the sample mean is found to be x  535 . Also, the

population standard deviation is

(a) Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit.

(b) Determine the P-value for this test. Show all work; writing the correct P-value, without supporting work, will receive no credit.

(c) Is there sufficient evidence to justify the rejection of H0 at the   0.01 level?

Explain. (20 pts)

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. The research conducted a survey, and found the following result:

In a random sample of 250 women, 70% said that the earth is getting warmer. In a random sample of 200 men, 67% said that the earth is getting warmer.

Assume we want to use a 0.05 significance level to test the claim.

(a) Identify the null hypothesis and the alternative hypothesis.

(b) Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit.

(c) Determine the critical value. Show all work; writing the correct critical value, without supporting work, will receive no credit.

(d) 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? Justify your conclusion. (25 pts)

Refer to the following data for Questions 28 and 29. :
x 0 - 1 1 2 4
y 3 - 2 3 6 8

28. Find an equation of the least squares regression line. Show all work; writing the correct

equation, without supporting work, will receive no credit. (15 pts)
29. Based on the equation from # 28, what is the predicted value of y if x = 3? Show all work
and justify your answer. (10 pts)

30. The UMUC Daily News reported that the color distribution for plain M&M's was: 35%
brown, 20% yellow, 20% orange, 15% 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.

Color Brown Yellow Orange Green Tan
Number 42 21 15 10 12
Assume we want to use a 0.10 significance level to test the claim that the published color
distribution is correct.
(a) Identify the null hypothesis and the alternative hypothesis.
(b) Determine the test statistic. Show all work; writing the correct test statistic, without
supporting work, will receive no credit.
(c) Determine the critical value. Show all work; writing the correct critical value,
without supporting work, will receive no credit.
(d) Is there sufficient evidence to support the claim that the published color distribution
is correct? Justify your answer. (25 pts)