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ECON154 Business Statistics

May Examinations 2024

Section A: Multiple-Choice Questions (45 marks)

1. You wish to make a pie chart displaying the share of individuals who have selected one of three options: A, B, or C. If you interview 250 people and 75 select C, how many degrees of the circle will C be?

A) 90

B) 180

C) 270

D) 144

2. You have received data on temperatures in Celsius/Fahrenheit in London during May 2023. What type of variable is temperature?

A) Nominal

B) Interval

C) Ordinal

D) Ratio

3. What is the median of the following numbers:

A) 8

B) 9

C) 7

D) 8.5

4. P(A) = 0.36, what is P(AC)

A) 0.47

B) 0.87

C) 0.74

D) 0.64

5. Data is normally distributed with mean=0 and variance=1. What is the skewness of this distribution?

A) 1.0

B) 0.5

C) 0.0

D) -0.5

6. Given the following scatter plot, the correlation between these two variables would be approximately what?

A) Positive

B) Negative

C) Zero

D) Independent

7. What is the probability a standard normal variable, Z, falls above 0.44?

A) 0.1700

B) 0.3300

C) 0.6700

D) 0.0934

8. If the probability of an event, R, is 0.6 and the probability of the intersection of event R and another event S is 0.3, what is the probability of S conditional on R?

A) 0.65

B) 4.00

C) 0.25

D) 0.50

9. What will be the relationship between the median and mean of the following distribution?

A) Mean = Median

B) Mean > Median

C) Mean < Median

D) Not enough information to say

10. A student's grade in a business course is comprised of attendance (5%), homework (20%), and a final exam (75%). Her scores for each of the categories are 70 (attendance), 95 (homework), 60 (final exam). Calculate her overall grade.

A) 90.0

B) 80.0

C) 67.5

D) Not enough information to say.

11. Two variables, P and S, have a covariance of -15. P has a variance of 9 and S has a variance of 25, what is the correlation coefficient between P and S?

A) 0.067

B) -1.00

C) 1.00

D) -0.067

12. In regression analysis, the variable that is being predicted is the

A) response, or dependent, variable

B) independent variable

C) intervening variable

D) is usually x

13. You have a binomial distribution where you draw 5 observations where the probability of success is 0.60. What is the standard deviation of this distribution?

A) 1.58

B) 1.37

C) 1.73

D) 1.09

14. A regression analysis between sales (in $1000) and price (in dollars) resulted in the following equation, where x is price and y is sales:

ŷ = 50,000 - 8x

The above equation implies that an

A) increase of $1 in price is associated with a decrease of $8 in sales

B) increase of $8 in price is associated with an increase of $8,000 in sales

C) increase of $1 in price is associated with a decrease of $42,000 in sales

D) increase of $1 in price is associated with a decrease of $8000 in sales

15. If the interquartile range is 60 and the third quartile is 34, beyond what value would we consider an observation an outlier?

A) 34

B) 96

C) 124

D) 94

Section B: Short-Answer Question (55 marks)

Short Answer 1 (30 points)

According to HealthX Institute, annual expenditure for prescription drugs is $838 per person in the country. A sample of 60 individuals from the Northwest region shows a per person annual expenditure for prescription drugs of $745. Use a population standard deviation of $300 to answer the following questions.

a)  Formulate the null and alternative hypotheses for a test to determine whether the sample data support the conclusion that the population annual expenditure for prescription drugs per person is lower in the Northwest than in the rest of the country. [5 points]

b)  Compute the value of the test statistic. [5 points]

c)  What is the p-value? [5 points]

d)  At α = 0.01, what is your conclusion? [5 points]

e)  What is a Type I error in this situation? [5 points]

f)   What is a Type II error in this situation [5 points]

Short Answer 2 (25 points)

The Dow Jones Industrial Average (DJIA) and the Standard & Poor’s 500 (S&P 500) indices are used as measures of stock market movement. Based on 15 weeks of closing prices for both DJIA and S&P 500, a regression equation was estimated by regressing the S&P500 closing price on the DJIA closing price as the independent variable. The following table provides the regression output:

a)  Develop the estimated regression equation. [5 points]

b)  Is there a significant relationship between S&P 500 closing price and DJIA closing price? Test for the significance at α = 0.05. [5 points]

c)  Does the estimated regression equation provide a good fit? Explain. [5 points]

d)  Suppose that the closing price for DJIA is 13,500. Predict the closing price for S&P 500. [5 points]

e)  Provide an interpretation for the slope of the estimated regression equation? [5 points]