Practice Test 1 Business Statistics

Practice Test 1 Business Statistics:

Name:______Date:______

Multiple Choice: Each is worth two points Identify the letter of the choice that best completes the statement or answers the question. **Skip 15-17,18,20 Ch10-12,13 Material

____ 1. The sum of the relative frequencies for all classes will always equal a. the sample size b. the number of classes c. one d. any value larger than one ____ 2. The interquartile range is a. the 50th percentile b. another name for the variance c. the difference between the largest and smallest values d. the difference between the third quartile and the first quartile ____ 3. The standard deviation of a sample of 100 observations equals 64. The variance of the sample equals a. 8 b. 10 c. 6400 d. 4,096 ____ 4. The numerical value of the standard deviation can never be a. larger than the variance b. zero c. negative d. smaller than the variance ____ 5. The set of all possible sample points (experimental outcomes) is called a. a sample b. an event c. the sample space d. a population ____ 6. A random variable that can assume only a finite number of values is referred to as a(n) a. infinite sequence b. finite sequence c. discrete random variable d. discrete probability function

1 Exhibit 5-11 A local bottling company has determined the number of machine breakdowns per month and their respective probabilities as shown below:

Number of Breakdowns Probability 0 0.12 1 0.38 2 0.25 3 0.18 4 0.07

____ 7. Refer to Exhibit 5-11. The probability of at least 3 breakdowns in a month is a. 0.5 b. 0.10 c. 0.30 d. 0.90 ____ 8. A normal probability distribution a. is a continuous probability distribution b. is a discrete probability distribution c. can be either continuous or discrete d. must have a standard deviation of 1

Exhibit 6-6 The starting salaries of individuals with an MBA degree are normally distributed with a mean of $40,000 and a standard deviation of $5,000.

____ 9. Refer to Exhibit 6-6. What percentage of MBA's will have starting salaries of $34,000 to $46,000? a. 38.49% b. 38.59% c. 50% d. 76.98% ____ 10. Given that Z is a standard normal random variable, what is the value of Z if the area between -Z and Z is 0.901? a. 1.96 b. -1.96 c. 0.4505 d. 1.65 ____ 11. Which of the following is not a measure of central location? a. mean b. median c. variance d. mode

2 ____ 12. The descriptive measure of dispersion that is based on the concept of a deviation about the mean is a. the range b. the interquartile range c. the absolute value of the range d. the standard deviation ____ 13. Which of the following symbols represents the mean of the population? a. 2 b.  c.  d. ____ 14. Which of the following symbols represents the size of the sample a. 2 b.  c. N d. n ____ 15. If two events are independent, then a. they must be mutually exclusive b. the sum of their probabilities must be equal to one c. their intersection must be zero d. None of these alternatives is correct.. ____ 16. Which of the following statements is(are) always true?

a. -1  P(Ei) 1 b. P(A) = 1 - P(Ac) c. P(A) + P(B) = 1 d. P  1 ____ 17. A measure of the average value of a random variable is called a(n) a. variance b. standard deviation c. expected value d. coefficient of variation ____ 18. Four percent of the customers of a mortgage company default on their payments. A sample of five customers is selected. What is the probability that exactly two customers in the sample will default on their payments? a. 0.2592 b. 0.0142 c. 0.9588 d. 0.7408 ____ 19. The expected value of a discrete random variable a. is the most likely or highest probability value for the random variable b. will always be one of the values x can take on, although it may not be the highest probability value for the random variable c. is the average value for the random variable over many repeats of the experiment d. None of these alternatives is correct. ____ 20. Which of the following is not a property of a binomial experiment? a. the experiment consists of a sequence of n identical trials b. each outcome can be referred to as a success or a failure c. the probabilities of the two outcomes can change from one trial to the next d. the trials are independent

3 Exhibit 5-9 The probability distribution for the daily sales at Michael's Co. is given below.

Daily Sales (In $1,000s) Probability 40 0.1 50 0.4 60 0.3 70 0.2

____ 21. Refer to Exhibit 5-9. The expected daily sales are a. $55,000 b. $56,000 c. $50,000 d. $70,000 ____ 22. For a standard normal distribution, the probability of z  0 is a. zero b. -0.5 c. 0.5 d. one

Exhibit 6-2 The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds.

____ 23. Refer to Exhibit 6-2. What percent of players weigh between 180 and 220 pounds? a. 28.81% b. 0.5762% c. 0.281% d. 57.62%

Exhibit 6-6 The starting salaries of individuals with an MBA degree are normally distributed with a mean of $40,000 and a standard deviation of $5,000.

____ 24. Refer to Exhibit 6-6. What is the probability that a randomly selected individual with an MBA degree will get a starting salary of at least $47,500? a. 0.4332 b. 0.9332 c. 0.0668 d. 0.5000 ____ 25. Larger values of r2 imply that the observations are more closely grouped about the a. average value of the independent variables b. average value of the dependent variable c. least squares line d. origin

4 ____ 26. If the coefficient of correlation is a positive value, then the slope of the regression line a. must also be positive b. can be either negative or positive c. can be zero d. can not be zero ____ 27. Regression analysis was applied between sales (in $1000) and advertising (in $100) and the following regression function was obtained.

= 500 + 4 X

Based on the above estimated regression line if advertising is $10,000, then the point estimate for sales (in dollars) is a. $900 b. $900,000 c. $40,500 d. $505,000 ____ 28. A regression analysis between demand (Y in 1000 units) and price (X in dollars) resulted in the following equation

= 9 - 3X

The above equation implies that if the price is increased by $1, the demand is expected to a. increase by 6 units b. decrease by 3 units c. decrease by 6,000 units d. decrease by 3,000 units

Exhibit 12 You are given the following information about y and x.

y x Dependent Variable Independent Variable 5 1 4 2 3 3 2 4 1 5

____ 29. Refer to Exhibit 12-2. The least squares estimate of b0 equals a. 1 b. -1 c. 6 d. 5

Short Answer/Problems

5 1.The following data represent the daily demand (y in thousands of units) and the unit price (x in dollars) for a product.

Daily Demand (y) Unit Price (x) 47 1 39 3 35 5 44 3 34 6 20 8 15 16 30 6

a. Compute and interpret the sample covariance for the above data. b. Compute and interpret the sample correlation coefficient.

2.The daily dinner bills in a local restaurant are normally distributed with a mean of $28 and a standard deviation of $6.

6 a. What is the probability that a randomly selected bill will be at least $39.10? b. What percentage of the bills will be less than $16.90? c. What are the minimum and maximum of the middle 95% of the bills? d. If twelve of one day's bills had a value of at least $43.06, how many bills did the restaurant collect on that day?

3.Below you are given a partial computer output based on a sample of 7 observations, relating an independent variable (x) and a dependent variable (y).

7 Predictor Coefficient Standard Error Constant 24.112 8.376 x -0.252 0.253

Analysis of Variance

SOURCE SS Regression 196.893 Error 94.822 a. Develop the estimated regression line. b. If you are given that x = 50, find the estimate of y based on your regression equation. c. Determine the coefficient of determination and interpret your answer.