Project #17633 - Distribution,regression,random sample,hypothesis, probability

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.

The frequency distribution below shows the distribution for checkout time (in minutes) in a MiniMart between 3:00 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 not less than 4 minutes?

2. Calculate the mean of this frequency distribution.

3. In what class interval must the median lie? Explain your answer. (You don’t have to find the median)

4. Assume that the smallest observation in this dataset is 1.2 minutes. Suppose this observation were incorrectly recorded as 0.2 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.

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 an even number. Let B be the event that the outcome of second roll is greater than 4.

5. What is the probability that the outcome of the second roll is greater than 4, given that the first roll is an even number?

6. Are A and B independent? Why or why not?

Refer to the following data to answer questions 7 and 8. 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:

4 14 15 17 20

7. Find the standard deviation.

8. Are any of these study times considered unusual in the sense of our textbook? Explain. Does this differ with your intuition? Explain.

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.

Minimun      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. Then explain your answer in each case.

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?

Refer to the following information for Questions 12 and 13.

There are 1000 students in the senior class at a certain high school. The high school offers two Advanced Placement math / stat classes to seniors only: AP Calculus and AP Statistics. The roster of the Calculus class shows 95 people; the roster of the Statistics class shows 86 people. There are 43 overachieving seniors on both rosters.

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

13. If the student is in the Statistics class, what is the probability the student is also in the Calculus class?

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.

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?

16. What is the probability that the three numbers drawn are all different?

17. What is the probability that the three numbers drawn are all odd numbers?

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.

19. Determine the standard deviation of x.

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?

22. Given a sample size of 64, with sample mean 730 and sample standard deviation 80, we perform the following hypothesis test. 0:750Hμ=

1:750Hμ<

What is the conclusion of the test at the 0.05α=level? Explain your answer.

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 is between 10 and 12 feet tall?

24. Find the 3rd quartile of the pecan tree height distribution.

25. If a random sample of 100 pecan trees is selected, what is the standard deviation of the sample mean?

26. Consider the hypothesis test given by 01:530:530.HHμμ=≠

In a random sample of 81 subjects, the sample mean is found to be 524.x=Also, the population standard deviation is 27.σ=

Determine the P-value for this test. Is there sufficient evidence to justify the rejection of 0H at the 0.01α= level? Explain.

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.

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

In a random sample of 220 men, 67% said that the earth is getting warmer.

At the 0.05 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? Show all work and justify your answer.

Refer to the following data for Questions 28 and 29.

x      0      -1      1        2       3

y       4      -2      5        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.

29. Based on the equation from # 28, what is the predicted value of y if x = 4? Show all work and justify your answer.

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. Show all work and justify your answer.

Color     Brown      Yellow    Orange    Green     Tan

Number    42          21         12          7           18

 Subject Mathematics Due By (Pacific Time) 11/24/2013 03:00 pm
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