statistics

Questions 1 – 3 refer to the histogram below which shows the gas mileage of a sample of cars.

Answer and Explanation
1. What percentage of the cars got less than 25 miles per gallon?
2. Is 19 a possible value of the median for the gas mileage data?
3. Suppose the largest value in this data set is 34.7 miles per gallon. If that was wrongly entered as 344.7 miles per gallon, what would happen to the size of

a) the mean

b) the median

Questions 4 – 6 refer to the boxplots below which display final exam scores for all students in two different sections of the same course.

For each of the following questions, write the letter of your answer AND explain why you think that is the correct answer (Answers with no explanation will not receive credit)

  1. A) Section A     B) Section B     C) Both sections are about equal     D) It is impossible to tell

           

Answer and Explanation
4. Which section has more students?
5. Which section has a greater percentage of students with scores at or above 80?
6. Which section has a greater percentage of students with scores at or above 55?

Questions 7 – 9: Read each of the research descriptions and decide which of the following would be the most appropriate display of the data collected from the research.

(A)   side-by-side boxplots       (B)   a histogram       (C)   a scatterplot      (D)   a two-way table

Write the letter of your choice AND an explanation of why you think it is correct. Your explanation should include a) identification of the explanatory and response variables and

  1. b) what type of variables they are.
Answer and Explanation
7. A researcher suspects that males and females prefer different colors in cars. He surveys 100 potential car buyers and records their gender and their color preference.
8. A market researcher for a cereal company thinks that the amount of shelf space the cereal gets in a supermarket impacts the weekly sales of the product. He selects a sample of 30 supermarkets and measures the amount of shelf space (in inches) and finds out the weekly sales (in $).
9. A different researcher at the same cereal company thinks that the shelf the cereal is displayed on (top, middle, or bottom) is more important in influencing weekly sales. She collects data from 30 supermarkets about which shelf the product is on and the weekly sales (in $).

Questions 10 – 20: Use the attached data set bbdata4.xls to answer these questions. Give your answers with at least 2 decimal places. (Be careful to follow the rules of rounding.)

Questions 10 – 15: For the variable Average Ticket Price (Average Ticket$), use Excel and/or a calculator to find the following:

10. median
11. mean
12. sample standard deviation
13. range
14. What is the shape of this distribution? Give a piece of evidence based on the statistics above to support your answer.
15. According to the IQR rule, are there any outliers?

·    Explain how you arrived at your answer.

·    If there are any outliers, identify the team(s).

Questions 16 – 20:  A sports writer knows that fans will generally pay more to see a winning team and wants to see if it is possible to use the number of wins in a season (Wins) to predict the average ticket price.  Use the data to create a scatterplot, add a trendline and request whatever additional information you need to answer the following questions:

16. Describe the overall pattern of the relationship between number of wins and average ticket price.
17. What is the equation for the least squares regression line for the relationship between number of wins and average ticket price?
18. Predict the average ticket price for a team that wins 75 games.
19. For every additional win a team gets, their average ticket price would be expected to _______ by ______.
20. What is the correlation between wins and average ticket price?

(numerical answer required)

Questions 21 – 29.

 

21. P(A) = .2 and P(B) = .5. If A and B are independent events, what is the P(A and B)?
22. P(A) = .2 and P(B )= .7. If A and B are Independent events, what is the P(A | B)?
23. The employees of a company were surveyed on questions regarding their educational background (college degree or no college degree) and marital status (single or married).

45% of the employees had college degrees

35% of the employees were single

15% of the employees were single and had college degrees

Fill in the two-by two table in the Answer column.

Use the following key:

C=college degree

No C = no college degree

S = single

M = married

Total
Total
24. a) How many variables are in the table you constructed in the question above?

b) Name the variables.

25. Use the information in Q 23.

What is the probability that an employee of the company is single or does not have a college degree?

26. Use the information in Q 23. If an employee is single, what is the probability the employee has a college degree?
27. At a different company, 600 of the 2000 employees are male. If two employees are randomly selected, what is the probability that they are the same gender?
28. A student is taking a very short multiple-choice quiz in which each question has 5 choices – – A, B, C, D, E. The student hasn’t studied so he randomly selects an answer for each of the 3 questions.

What is the probability that he gets all 3 questions correct?

29. What is the probability that the student in the previous question gets at least one answer correct?
30. The probability that a new advertising campaign will increase sales is 0.80. The probability that the cost of developing the new ad campaign can be kept within the original budget allocation is 0.5. Assuming that the two events are independent, the probability that the cost is kept within budget or that the campaign will increase sales is ______.
For questions 31 – 33, which one of the following sampling methods best matches the description? Explain your choice.

A) Stratified    B) Simple Random    C) Cluster    D) Systematic

Answer and Explanation
31. Citibank wants to survey its employees. 25 branches are randomly selected and all of the employees in those branches are given the survey.
32. From a list of all Walmart employees, the research staff divides the list into full-timers and part-timers and randomly selects a sample of 500 from each group.
33. Each morning, Mission Motors uses a random number generator to select the first car for inspection and then inspects every 15th car coming off the production line for possible defects.
34. Two CUNY students are randomly selected.

Let A represent the event “the first student lives in Queens.”

Let B represent the event “the second student lives in Queens.”

Are the events A and B disjoint? Explain your answer.

35. Referring to the question above, are the events A and B independent? Explain your answer.
36. P(A) =.3 and P(B)= .7. If A and B are disjoint events, what is the P(A and B)?
37. A business owner is starting a new ad campaign. She decides to advertise for 4 months as long as the monthly revenue for her business results in a profit. She will stop advertising as soon as the monthly revenue does not result in a profit.

Let P = profit; Let N = no profit.

What is the sample space for this situation?

38. The correlation (r) between Variable A and Variable B = 0. Does this mean that no relationship exists between A and B? Explain your answer.
39. Questions 39 and 40 are based on the following table:

               Job Application Outcome

 

Applicant Age  

Hired

 

Not hired

 

Total

Younger than 40 79 1165 1244
40 or older 27 189 216
Total 106 1354 1460

For the table above, would it be more appropriate to calculate conditional row percentages or conditional column percentages? Explain your answer.

40.

               Job Application Outcome

 

Applicant Age  

Hired

 

Not hired

 

Total

Younger than 40      
40 or older      
Total      

a)    Fill in the table with the appropriate percentages.

b)    Provide an explanation of what the data shows.

 
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