MAT 117 MAT117 Final Exam with Answers (Pace University)

MAT 117 MAT/117 MAT117 FINAL EXAM (PACE UNIVERSITY)

Questions 1–3: The following output are MegaStat analyses of score on a class’ exam.

Descriptive statistics

#1

count 20 mean 49.90 sample standard deviation 21.36 sample variance

minimum
maximum 84 range 68

Frequency Distribution - Quantitative

Data cumulative
upper midpoint width frequency percent frequency percent

70<8577

20 100.0

1. What is the minimum data value?
2. What is the class midpoint of the class [25, 40)
3. What is the relative cumulative frequency of the class [55, 70)
4. The following is a list of five of the world's busiest airports by passenger traffic for 2010.

lower

10 <2518
25 <40
40 <5548
55<7063 525.015

3 15.0 3 15.0 20.0 7 35.0

50.0 5 25.0 20 100.0

3 15.0

Name Hartsfield-Jackson Capital International London Heathrow O’Hare
Tokyo

True or False: This data

Location
Atlanta, Georgia, United States Beijing, China
London, United Kingdom Chicago, Illinois, United States Tokyo, Japan

# of Passengers (in millions) 89
74
67

66 64

can be best represented by a histogram?

1. Suppose that, on average, electricians earn approximately  = 54 000 dollars per year in the United States. Assume that the distribution for electrician's yearly earnings is normally dis- tributed and that the standard deviation is  = 12 000 dollars.What is the probability that the average salary of four randomly selected electricians exceeds $60,000?
2. The snowfall (in inches) during the month of January in a particular geographic region is nor- mally distributed with a standard deviation of 16.75. In the last 12 years, the sample average of snowfall is computed as 122.50. Construct a 90% confidence interval of the average snow- fall in this region.
3. A professional sports organization is going to implement a test for steroids. The test gives a positive reaction in 94% of the people who have taken the steroid. However, it erroneously gives a positive reaction in 4% of the people who have not taken the steroid. What is the prob- ability of a Type I and Type II error using the null hypothesis “the individual has not taken ste- roids.”

A. Type I: 4%, Type II: 6% B. Type I: 6%, Type II: 4% C. TypeI:94%,TypeII:4% D.TypeI:4%,TypeII:94%

8. A fast-food franchise is considering building a restaurant at a busy intersection. A financial advisor determines that the site is acceptable only if, on average, more than 300 automobiles pass the location per hour. The advisor tests the following hypotheses: Ho:   300 vs. Ha:

  300 . The consequences of committing a Type I error would be that _______________.

A. The franchiser builds on an acceptable site
B. The franchiser builds on an unacceptable site
C. The franchiser does not build on an acceptable site D. The franchiser does not build on an unacceptable site

9. Many cities around the United States are installing LED streetlights, in part to combat crime by improving visibility after dusk. An urban police department claims that the proportion of crimes committed after dusk will fall below the current level of 0.84 if LED streetlights are installed. Specify the null and alternative hypotheses to test the police department's claim.

A. Ho:p = 0.84 vs.Ha: p0.84 B.Ho: p0.84 vs.Ha: p0.84 C. Ho: p0.84 vs.Ha: p0.84 D.Ho: p0.84 vs.Ha: p0.84

Questions 10–13: In August of 2010, Massachusetts enacted a 150-day right-to-cure period that mandates that lenders give homeowners who fall behind on their mortgage an extra five months to become current before beginning foreclosure proceedings. Policymakers claimed that the policy would result in a higher proportion of delinquent borrowers becoming current on their mortgages. To test this claim, researchers took a sample of 244 homeowners in danger of foreclosure in the time period surrounding the enactment of this law. Of the 100 who fell behind just before the law was enacted, 30 were able to avoid foreclosure, and of 144 who fell behind just after the law was enacted, 48 were able to avoid foreclosure. Let pB and pArepresent the proportion of delinquent borrowers who avoid foreclosure just before and just after the right-to-cure law is enacted, respec- tively.

10. State the null and alternative hypothesis will test the policymakers' claim.

11. What test statistic should be used to test the hypothesis? Give the formula. Questions 12 & 13: Below is a partial MegaStat output base upon the data.

Hypothesis test for two independent proportions

p1 p2

0.3 0.3333 30/100 48/144 30. 48. 100 144

-0.0333 0. 0.0607 -0.55

12. What is the p-value of the test?

13. Should you accept or reject the null hypothesis based upon a 5% level of significance? Explain.

Questions 14–16: A new sales training program has been instituted at a rent-to-own company. Prior to the training, 10 employees were tested on their knowledge of products offered by the company. Once the training was completed, the employees were tested again in an effort to determine whether the training program was effective. Scores are known to be normally distributed. The sample scores on the tests are listed next.

pc

0.3197 p (as decimal) 78/244 p (as fraction)

78. X 244 n

difference hypothesized difference std. error
z

Pre-test Score 66
94
87

84 76 88

Post-test Score 75

100 93 85 75 90

14. What are the appropriate hypotheses to determine if the training increases scores? 15. What test statistic should be used to test the hypotheses? Give its formula?
16. What degree of freedom does the test statistic have?

Questions 17–20: A farmer uses a lot of fertilizer to grow his crops. The farmer's manager thinks fertilizer products from distributor A contain more of the nitrogen that his plants need than distributor B's fertilizer does. He takes two independent samples of four batches of fertilizer from each distributor and measures the amount of nitrogen in each batch. Fertilizer from distributor A contained 23 pounds per batch and fertilizer from distributor B contained 18 pounds per batch. Suppose the population standard deviation for distributor A and distributor B is four pounds per batch and five pounds per batch, respectively. Assume the distribution of nitrogen in fertilizer is normally distributed. Let A and B represent the average amount of nitrogen per batch for fertilizer's A and B, respectively.

1. What null and alternative hypotheses should the farmer use?
2. What test statistic should the farmer use to test the above hypotheses? Give its formula.
3. What critical value should the farmer use to test the above hypotheses at the 10% level of sig- nificance?
4. Assuming the test statistic has a value of 1.5617, should the null hypothesis be accepted or rejected at the 10% level of significance?
5. Suppose you want to perform a test to compare the mean GPA of all freshmen with the mean GPA of all sophomores in a college? What type of sampling is required for this test?

1. Independent sampling with qualitative data
2. Independentsamplingwithquantitativedata
3. Matched-pairs sampling with qualitative data
4. Matched-pairs sampling with quantitative data

1. True or False: The null hypothesis Ho: 2  10 is rejected at the 5% level of significance if the value of the test statistic exceeds 2 .
2. For a sample of 10 observations drawn from a normally distributed population, we obtain the sample mean and the sample variance as 50 and 75, respectively. We want to determine whether the population variance is greater than 70. The critical value at a 5% significance level is:

A. 16.919 B. 9.642 C. 3.325 D. 1.645 E. None of these.

24. The chi-square test of a contingency table is a test of independence for:

A. A single qualitative variable B. Two qualitative variables
C. Twoquantitativevariables D.Threeormorequantitativevariables

25. The chi-square test of a contingency table is valid when the expected cell frequencies are:

A. Equal to 0 B. More than 0 but less than 5 C. Atleast5 D.Negative

0.025

26. True or False: Another name for an explanatory variable is the dependent variable.

Questions –: The following table shows the cross-classification of a random sample of compa- nies’ accounting practices (either straight line, declining balance, or both) and country (either France, Germany, or UK).

Accounting Practice Straight line

Declining Balance Both
Total

Country France Germany UK

Observed 30 Expected 22.535 (O-E)_/E 2.473 Observed 15 Expected 16.624 (O - E)_ / E

Observed 13 Expected 18.841 (O-E)_/E 1.811 Observed 49 50 58 Expected 49.000 50.000 58.000 (O - E)_ / E 0.102 6.661 4.442

11.205chi-square df

.0244p-value

Total

61 61.000 6.177 45 45.000 0.353 51 51.000 4.675 157 157.000 11.205

27. What would be the appropriate null and alternative hypotheses for the test above?

1. What are the expected number of companies from Germany that use a Declining Balance Accounting Method?
2. What is the cell chi-square for UK companies that use Declining Balances.
3. What is the degree of freedom for the test statistic?
4. Should accept or reject the null hypothesis at the 5% level of significance?
5. Explain that the meaning of the answer above in everyday English.

 Look at the scatterplot of the values of two random variables. Describe their linear relation- ship?

A. No relationship. B. Strong and negative. C. Strong and positive. D. Weak and positive. E. Weak and negative.

Questions 34–36: Attached is a MegaStat printout. The analysis tries to forecast the value of a home (in thousands of dollars) from the number of bathrooms in the home:

Regression Analysis

r2 0.385 r 0.620 Std. Error of Estimate26.086

n24

k1 Dep. Var.Value

Regression output

variables

Intercept

coefficients

a = 254.473

b = 44.454

std. error

11.982

t (df=22)

3.710

p-value

confidence interval

95% lower

19.605

95% upper

69.303

Bathrooms

34. What is the equation of the regression line?
35. What is the predicted value of a home with two bathrooms? Express your answer in dollars. 36. Do you think that more bathrooms increase the value of a home? Please explain. (6 points)