Statistics Quiz

Very important statistics quiz. I need it completed within 28 hrs. Please review and if you are Certain, ONLY if you are CERTAIN, that you can handle the assignment then please let me know what you would be willing to complete this for. Thank you 

Youmust answer all

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2 questions to get the maximum score of 100 points. Make sure your answers are as complete as possible and show your work or argument. In particular, when there are calculations involved, you should show how you come up with your answers with critical work or necessary tables. Solutions that come directly from program software packages will not be accepted.

It’s due by midnight, Sunday November 17 (Maryland time)

1. (4 points)

An internet service ran a survey of its users and asked if they preferred a real Christmas tree or a fake one. They received 6431 responses, and 3852 of them preferred a real tree. Given that 3852 is 59.9% of 6431, can we conclude that about 60% of people who observe Christmas prefer a real tree? Why or why not?

2. (4 points)

An editorial in a magazine reported that adding a certain detergent to a load of laundry would reduce stains by 150%. What is wrong with this statement?

3. (5 points)

A supermarket is considering expanding its services by adding a pharmacy, but prior to doing so it will use a survey to determine the extent to which its customers are interested in such a service. The employees suggested four different survey procedures:

(a) Ask customers to voluntarily phone in their preferences;

(b) Ask customers to voluntarily mail in their preferences;

(c) Survey a selection of people whose names are randomly chosen from a list of all customers; or

(d) Survey a selection of people whose names are randomly chosen from the telephone directory.

Which survey procedure do you think would be the most appropriate for obtaining a statistically unbiased sample? Please explain your answer.

4. (5 points)

The following graph shows the population of Washington D.C., in 2000 and in 2010. What is wrong with this graph? Draw a graph that depicts the data in a fair and objective way.

5. (20 points)

A UMUC professor teaching Stat 200 was interested in knowing how much time students spend in MyMathLab doing homework for Chapter 4. Fortunately, MyMathLab provides the time worked, per student, for each assignment. She recorded the times of 29 students as follows:

2.6, 2.8, 2.3, 3.4, 2.7, 2.7, 2.8, 2.4, 2.4, 2.6, 2.4, 3.0, 3.2, 3.1,

2.1, 2.3, 3.6, 3.7, 2.3, 2.6, 2.7, 2.7, 2.4, 2.9, 2.5, 2.7, 2.6, 2.9, 2.9

Note, that even though we are talking about time, these measurements are decimal numbers. So, for example, 0.5 = 30 minutes.

(a) Prepare a frequency distribution with a class width of 0.2 hours, and another with a class width of 0.5 hours

(b) Construct a histogram with a class width of 0.2, and another with a class width of 0.5.

(c) Give a 5-number summary of the hours spent doing homework for Chapter 4, and construct the corresponding boxplot.

(d) Of course, it is always nice to have the benefit of the raw data. With the given list of 29 time figures, you can easily determine the mean mass of the sample. But what if you do not have access to the raw data? What if all you have are the frequency distributions?

Now pretend that you are only given the frequency distribution or histogram, and that you are asked to calculate the mean number of hours that students spend on Chapter 4 homework. Use what you got in (a) and/or (b) to determine the mean number of hours. Do it with frequency table/histogram with class width of 0.2 hours, and again with 0.5 hours. Compare your results to the ‘actual’ mean mass.

6. (10 points)

The mean height of 8 year old girls in my daughter’s school is 125 cm, with a standard deviation of 0.3, and the height has a bell-shaped distribution.

(a) What is the approximate percentage of girls between 124.4 cm and 125.6 cm?

(b) What is the approximate percentage of girls between 124.1 cm and 125.9 cm?

7. (6 points)

A number is selected at random from the first forty natural numbers. What is the probability that it is a multiple of either 4 or 11?

8. (10 points)

Imagine that you are a participant in a game show, where “free” money is given away. There are 4 prizes hidden on a game board with 16 spaces. One prize is worth $4000, another is worth $1500, and two are worth $1000 each.

If you select one of the prize spaces, you will get the related prize. However, if you select any of the other spaces, you will have to pay $50, as penalty for not making the ‘wise’ choice

In this game show, you are given a choice:

· Choice #1: You are offered a sure prize of $400 in cash. You can take the money and leave.

· Choice #2: Take your chance and play the game.

What would be your choice? Take the money and run, or play the game? Please explain your decision. Remember that this is a statistics test. Do not just go with your gut feeling – find in the material we learned a tool that can help make a decision based on calculation.

9. (9 points)

In the judicial case of United States v. City of Chicago, discrimination was charged in a qualifying exam for the position of Fire Captain. In the table below, Group A is a minority group and Group B is a majority group.

Passed

Failed

Group A
Group B

10
417

14
145

(a) If one of the test subjects is randomly selected, find the probability of getting someone who passed the exam.

(b) Find the probability of randomly selecting two different test subjects and finding that they are both in Group A.

(c) Find the probability of getting someone who passed, given that the selected person is in Group A.

10. (7 points)

The office manager has decided that dress code is needed for office unity. All office staff are required to wear either blue shirts or red shirts. There are 10 men and 6 women working in the office. On a particular day, 6 men wore blue shirts, and 4 others wore red shirts, whereas 4 women wore blue shirts and 2 others wore red shirts.

Apply the Addition Rule to determine the probability of finding men or people wearing blue shirt in the office that day.

11. (10 points)

I have 5 gem-quality crystals in my home collection. Their weights, in carats, are 23.5, 14.6, 30.6, 10.8, and 28.3.

(a) Are the gems in my collection a sample? Or are they the whole population of gems in my collection? Your answer will determine the formulas you use in the following

(b) What is the variance in weight of my gem collection?

(c) What is the standard deviation in weight of my gem collection?

(d) What are the coefficients of variation in weight of my gem collection?

12. (10 points)

Most of us hate buying peaches that were picked too early. Unfortunately, waiting to pick peaches until they are almost ripe carries a risk of having 8% of the picked peaches rot when they arrive at the packing facility. If the packing process is all done by machines without human inspection to pick out any rotten peaches, what would be the probability of having at most 2 rotten peaches packed in a box of 12?

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