Business Statistics: Review Solutions, Questions & Answers - Chapter 3 Review PDF

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STAT2201 Business Statistics

Chapter 3 Review Solutions 1.

Review Questions Below is the data from a sample of 8 people recording the number of years remaining on their mortgages: 9

8

10

10

12

6

11

10

a. Compute the mean, 9.5; median, 10; and mode 10. Ordered 6 8 9 10 10 10 11 12 list b. Using your calculator keys determine the range 12-6 = 6; standard deviation (sx) 1.8516; variance (sx)2 3.4286. 2.

For the 23 data values below, compute: Ordered List 32 32 32 40 40 42 46 52 52

37 46 52

37 46 52

40 46 58

40 46 72

40 46

25

(23) = 5.75 round to 6 = 40) a. Q1 (25th percentile 𝑖 = 100 th Q2 (50 percentile, or median, is in position 12 = 46), Q3 (75th percentile is in position 18 = 52) minimum maximum range

32 72 40

1st quartile (Q1) Median (Q2) 3rd quartile (Q3)

b. low outliers high outliers

40.00 46.00 52.00

Q1-1.5(IQR) 70

IQR (Q3 – Q1 = 12); and determine any outliers 72 c. Construct a box plot BoxPlot

30

35

40

45

50

55

60

65

70

75

Row1

d. Is there any skew? NO. If so, in what direction and why? The distribution is nearly symmetrical.

3.

Assume that the evaluations in a business statistics course consist of 2 quizzes each worth 15%, a midterm exam worth 30%, and a final exam worth 40%. Nathan, a student in this course, received the following grades throughout the semester; help Nathan compute his course grade: Quiz 1 80% score 80 76 82 75

4.

Midterm Exam 82%

Final Exam 75%

score x weight weight 0.15 12.00 0.15 11.40 0.30 24.60 0.40 30.00 Average = 78.00

The table below gives statistics relating to a hypothetical 10-year record of two portfolios. Compute the appropriate measure to determine which fund has less risk.

𝐶𝑉 = 𝐶𝑉𝐴 = 5.

Quiz 2 76%

𝑠 𝑥  22.8 15.3

Lower CV implies lower volatility and therefore less risk = 1.49

𝐶𝑉𝐵 =

15.9 10.2

= 1.56

∴ Portoflio A has less risk

The mean monthly mortgage paid by all home owners in a city is $2365 with a standard deviation of $340. The distribution of mortgage payments is symmetric and bell-shaped. The shape of the distribution (symmetrical bell-shape) allows us to apply the Empirical Rule to estimate the required percentages or intervals: a. Find the percentage of all home owners in the city who pay a monthly mortgage in the interval $1685 to $3045. The interval is ±2 s.d. around the mean ∴ contains ≈ 95% b. Find the percentage of all home owners in the city pay who a monthly mortgage of $1345 to $3385. The interval is ±3 s.d. around the mean ∴ contains ≈ 100% c. Find the interval that contains the monthly mortgage payments of approximately 68% of all home owners. The interval that contains ≈ 68% is ±1 s.d. around the mean ∴ $2025 ↔$2705

6.

Suppose a particular brand of automobile tire has a mean life of 100,000 km and a standard deviation of 10,000, and that the tire life follows a bell-shaped symmetric distribution. Within how many kilometers can one expect 95% of these tires to last? What rule are you applying and why? The shape of the distribution (symmetrical bell-shape) allows us to apply the Empirical Rule to estimate the required percentages or intervals: The necessary interval is ±2 s.d. around the mean since it will contain ≈ 95% of the data, ∴ (100,000 – 2*(10,000)) ↔ (100,000 + 2*(10,000)); 80,000 km ↔ 120,000 km

Multiple Choice Review Questions 7. The owner of a company has recently decided to raise the salary of one employee, who was already making the highest salary, by 20%. Which of the following is(are) expected to be affected by this raise? A. Mean only B. Median only C. Mean and median only D. Mean, median, and mode 8.

The Boom company has recently decided to raise the salaries of all employees by 10 percent. Which of the following is(are) expected to be affected by this raise? A. Mean and mode only B. Mean and median only C. Mode and median only D. Mean, median, and mode

9.

If a box plot has the median left of center and the right whisker longer than the left whisker, then the distribution is: A. positively skewed. B. negatively skewed C. symmetric. D. none of these answers

10. What is/are the characteristic(s) of the coefficient of variation? A. It adjusts for differences in the magnitude of means. B. It has the same units of measurement as the observations. C. It allows for direct comparisons across different data sets. D. It adjusts for differences in the magnitude of means and It allows for direct comparisons across different data sets.

11. A z-score: A. is unitless. B. has the same units as the data. C. has the square of the same units as the data. D. none of the answers.

12. Professors at a local university earn an average salary of $80,000 with a standard deviation of $6,000. The salary distribution is approximately bellshaped. Because of budget limitations, it has been decided that only those whose salaries are approximately in the bottom 2.5% would get a raise. What is the maximum current salary that qualifies for the raise? A. About $58,000 µ=80,000 σ=6,000 95% is 2σ B. About $62,000 C. About $68,000 D. About $74,000 2.5%

95% 80,000

2.5%

80,000 – 2(6,000) = 68,000

13. Professors at a local university earn an average salary of $80,000 with a standard deviation of $6,000. The salary distribution is approximately bellshaped. What is the z-score for a faculty member with a salary of $100,000? A. About -3.33 B. About 3.33 𝑥 − 𝑥 100,000 − 80,000 = 3.33 𝑧= = C. About 1.172 6,000 𝑠 D. About -1.175

14. An investor bought common stock of Blackstone Company on several occasions at the following prices.

The average price per share at which the investor bought these shares of common stock was closest to: A. B. C. D.

$28.00 $29.43 $30.67 $31.00

∑(𝑤𝑖 𝑥𝑖 ) ∑ 𝑤𝑖 (100)(34) + (200)(30) + (400)(28)

𝑥 = =

100 + 200 + 400 20,600 = = 29.4286 700

15. If a sample covariance equals 2.35, this indicates 1 A. a positive linear relationship between two variables B. a negative linear relationship between two variables C. no linear relationship between two variables D. a strong linear relationship between two variables

16. If a sample correlation coefficient equals -0.92, this indicates A. a positive linear relationship between two variables B. a negative linear relationship between two variables C. no linear relationship between two variables D. a strong negative linear relationship between two variables...