**1. True or False. Justify for full credit. **

(a) The normal distribution curve is always symmetric to its mean.

(b) If the variance from a data set is zero, then all the observations in this data set are identical.

(c) P(A AND A^C ) 1, where A^C is the complement of A.

(d) In a hypothesis testing, if the p-value is less than the significance level α, we do not have sufficient evidence to reject the null hypothesis.

(e) The volume of milk in a jug of milk is 128 oz. The value 128 is from a discrete data set.

Refer to the following frequency distribution for Questions 2, 3, 4, and 5. Show all work. Just the answer, without supporting work, will receive no credit.

A random sample of 25 customers was chosen in UMUC MiniMart between 3:00 and 4:00 PM on a Friday afternoon. The frequency distribution below shows the distribution for checkout time (in minutes).

Checkout Time (in minutes) Frequency Relative Frequency

1.0 – 1.9 2

2.0 – 2.9 8

3.0 – 3.9

4.0 – 4.9 5

Total 25

2. Complete the frequency table with frequency and relative frequency.

3. What percentage of the checkout times was less than 3 minutes?

4. In what class interval must the median lie? Explain your answer.

5. Assume that the largest observation in this dataset is 5.8. Suppose this observation were incorrectly recorded as 8.5 instead of 5.8. Will the mean increase, decrease, or remain the same? Will the median increase, decrease or remain the same? Why?

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

2 15 15 18 30

Find the sample standard deviation. (Round the answer to two decimal places. Show all work. Just the answer, without supporting work, will receive no credit.)

Refer to the following information for Questions 7, 8, and 9. Show all work. Just the answer, without supporting work, will receive no credit.

A fair coin is tossed 4 times.

7. How many outcomes are there in the sample space?

8. What is the probability that the third toss is heads, given that the first toss is heads? (10 pts)

9. Let A be the event that the first toss is heads, and B be the event that the third toss is heads. Are A and B independent? Why or why not?

Refer to the following situation for Questions 10, 11, and 12.

The boxplots below show the real estate values of single family homes in two neighboring cities, in thousands of dollars.

For each question, give your answer as one of the following: (a) Tinytown; (b) BigBurg; (c) Both cities have the same value requested; (d) It is impossible to tell using only the given information. Then explain your answer in each case.

10. Which city has greater variability in real estate values?

11. Which city has the greater percentage of households with values $85,000 and over?

12. Which city has a greater percentage of homes with real estate values between $55,000 and $85,000?

Refer to the following information for Questions 13 and 14. Show all work. Just the answer, without supporting work, will receive no credit.

There are 1000 juniors in a college. Among the 1000 juniors, 200 students are taking STAT200, and 100 students are taking PSYC300. There are 50 students taking both courses.

13. What is the probability that a randomly selected junior is taking at least one of these two courses?

14. What is the probability that a randomly selected junior is taking PSYC300, given that he/she is taking STAT200?

15. UMUC Stat Club is sending a delegate of 2 members to attend the 2015 Joint Statistical Meeting in Seattle. There are 10 qualified candidates. How many different ways can the delegate be selected?

16. Imagine you are in a game show. There are 4 prizes hidden on a game board with 10 spaces. One prize is worth $100, another is worth $50, and two are worth $10. You have to pay $20 to the host if your choice is not correct. Let the random variable x be the winning. Show all work. Just the answer, without supporting work, will receive no credit.

(a) What is your expected winning in this game?

(b) Determine the standard deviation of x. (Round the answer to two decimal places)

17. Mimi just started her tennis class three weeks ago. On average, she is able to return 20% of her opponent’s serves. Assume her opponent serves 8 times. Show all work. Just the answer, without supporting work, will receive no credit.

(a) Let X be the number of returns that Mimi gets. As we know, the distribution of X is a binomial probability distribution. What is the number of trials (n), probability of successes (p) and probability of failures (q), respectively?

(b) Find the probability that that she returns at least 1 of the 8 serves from her opponent.

(c) How many serves can she expect to return?

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

The IQ scores are normally distributed with a mean of 100 and a standard deviation of 15.

18. What is the probability that a randomly person has an IQ between 85 and 115?

19. Find the 90th percentile of the IQ distribution.

20. If a random sample of 100 people is selected, what is the standard deviation of the sample mean?

21. A random sample of 100 light bulbs has a mean lifetime of 3000 hours. Assume that the population standard deviation of the lifetime is 500 hours. Construct a 95% confidence interval

estimate of the mean lifetime. Show all work. Just the answer, without supporting work, will receive no credit.

22. Consider the hypothesis test given by

H_0: p = 0.5

H_1: p < 0.5

In a random sample of 225 subjects, the sample proportion is found to be pˆ= 0.51.

(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 H_0 at the ɑ = 0.01 level? Explain.

**23. A new prep class was designed to improve AP statistics test scores. Five students were selected at random. The numbers of correct answers on two practice exams were recorded; one before the class and one after. The data recorded in the table below. We want to test if the numbers of correct answers, on average, are higher after the class.**

Is there evidence to suggest that the mean number of correct answers after the class exceeds the mean number of correct answers before the class?

Assume we want to use a 0.01 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 p-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 mean number of correct answers after the class exceeds the mean number of correct answers before the class? Justify your conclusion.

A random sample of 4 professional athletes produced the following data where x is the number of endorsements the player has and y is the amount of money made (in millions of dollars).

(a) Find an equation of the least squares regression line. Show all work; writing the correct equation, without supporting work, will receive no credit.

(b) Based on the equation from part (a), what is the predicted value of y if x = 4? Show all work and justify your answer.

**25. Randomly selected nonfatal occupational injuries and illnesses are categorized according to the day of the week that they first occurred, and the results are listed below. Use a 0.05 significance level to test the claim that such injuries and illnesses occur with equal frequency on the different days of the week. Show all work and justify your answer.**

(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 p-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 such injuries and illnesses occur with equal frequency on the different days of the week? Justify your answer.

**26 .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)

**Here’s the SOLUTION**