# Show all work

1. True or False. Justify/Show all work

(a) If there is no linear correlation between two variables, then these two variables are not related in any way.

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

(c) . P=(A-A) Where A is the complement of A.

(d) In a hypothesis testing, if the P-value is less than the significance level α, we 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.

Checkout Time

Frequency min.

1.0 - 1.9 2

2.0 - 2.9 12

3.0 - 3.9 2

4.0 - 4.9 4

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

3. In what class interval must the med***** *****e? Explain your answer.

4. Calculate the mean of this frequency distribution.

5. Calculate the standard deviation of this frequency distribution. (Round the answer to two decimal places)

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

2 15 15 18 40

6. Find the sample standard deviation. Round the answer to two decimal places

7. Find the coefficient of variation.

8. Are any of these study times considered unusual based on the Range Rule of Thumb? Show work/ explain.

Consider selecting one card at a time from a 52-card deck. Let event A be the first card is an ace, and event B bethe second card is an ace. (Note: There are 4 aces in a deck of cards)

9. If the card selection is without replacement, what is the probability that the first card is an ace and the second card is also an ace? Express the answer in simplest fraction form

10. If the card selection is with replacement, what is the probability that the first card is an ace and the second card is also an ace? Express the answer in simplest fraction

11. Are A and B independent when the selection is with replacement? Why

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.

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

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

14. UMUC Stat Club must appoint a president, a vice president, and a treasurer. There are 10 qualified candidates. How many different ways can the officers be appointed?

15. Mimi has seven books from the Statistics is Fun series. She plans on bringing three of the seven books with her in a road trip. How many different ways can the three books be selected?

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

x -1 0 1 2

() Px 0.1 0.3 0.4 0.2

16. Determine the expected value of x.

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

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. 18-20

18. 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?

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

20. How many serves can she expect to return?

The heights of dogwood trees are normally distributed with a mean of 9 feet and a standard deviation of 3 feet.. 21-23

21. What is the probability that a randomly selected dogwood tree is greater than 12 feet? (5 pts)

22. Find the 75th percentile of the dogwood tree height distribution. (10 pts)

23. If a random sample of 36 dogwood trees is selected, what is the probability that the mean height of this sample is less than 10 feet?

24. 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.

= a25. Given a sample size of 100, with sample mean 730 and sample standard deviation 100, we perform the following hypothesis test at the level. 0.05

HHmm =¹750 : 750 : 10

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

(b) Determine the critical values. 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.

26. Consider the hypothesis test given by

pH p H=<5.0: 5 .0: 10

p=In a random sample of 225 subjects, the sample proportion is found to be . 51.0ˆ

(a) Determine the test statistic. Show all work;

(b) Determine the P-value for this test.

= a(c) Is there sufficient evidence to justify the rejection of at the level? Explain. 0 H0.01

(a) If there is no linear correlation between two variables, then these two variables are not related in any way.

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

(c) . P=(A-A) Where A is the complement of A.

(d) In a hypothesis testing, if the P-value is less than the significance level α, we 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.

Checkout Time

Frequency min.

1.0 - 1.9 2

2.0 - 2.9 12

3.0 - 3.9 2

4.0 - 4.9 4

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

3. In what class interval must the med***** *****e? Explain your answer.

4. Calculate the mean of this frequency distribution.

5. Calculate the standard deviation of this frequency distribution. (Round the answer to two decimal places)

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

2 15 15 18 40

6. Find the sample standard deviation. Round the answer to two decimal places

7. Find the coefficient of variation.

8. Are any of these study times considered unusual based on the Range Rule of Thumb? Show work/ explain.

Consider selecting one card at a time from a 52-card deck. Let event A be the first card is an ace, and event B bethe second card is an ace. (Note: There are 4 aces in a deck of cards)

9. If the card selection is without replacement, what is the probability that the first card is an ace and the second card is also an ace? Express the answer in simplest fraction form

10. If the card selection is with replacement, what is the probability that the first card is an ace and the second card is also an ace? Express the answer in simplest fraction

11. Are A and B independent when the selection is with replacement? Why

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.

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

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

14. UMUC Stat Club must appoint a president, a vice president, and a treasurer. There are 10 qualified candidates. How many different ways can the officers be appointed?

15. Mimi has seven books from the Statistics is Fun series. She plans on bringing three of the seven books with her in a road trip. How many different ways can the three books be selected?

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

x -1 0 1 2

() Px 0.1 0.3 0.4 0.2

16. Determine the expected value of x.

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

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. 18-20

18. 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?

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

20. How many serves can she expect to return?

The heights of dogwood trees are normally distributed with a mean of 9 feet and a standard deviation of 3 feet.. 21-23

21. What is the probability that a randomly selected dogwood tree is greater than 12 feet? (5 pts)

22. Find the 75th percentile of the dogwood tree height distribution. (10 pts)

23. If a random sample of 36 dogwood trees is selected, what is the probability that the mean height of this sample is less than 10 feet?

24. 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.

= a25. Given a sample size of 100, with sample mean 730 and sample standard deviation 100, we perform the following hypothesis test at the level. 0.05

HHmm =¹750 : 750 : 10

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

(b) Determine the critical values. 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.

26. Consider the hypothesis test given by

pH p H=<5.0: 5 .0: 10

p=In a random sample of 225 subjects, the sample proportion is found to be . 51.0ˆ

(a) Determine the test statistic. Show all work;

(b) Determine the P-value for this test.

= a(c) Is there sufficient evidence to justify the rejection of at the level? Explain. 0 H0.01

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