Practice Test 1 Business Statistics:
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
____
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
____
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. ?
____
14. Which of the following symbols represents the size of the sample
a. ?2
d.
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
____
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
Short Answer/Problems
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 39 35 44 34 20
1 3 5 3 6 8
15 30
16 6
a. b.
Compute and interpret the sample covariance for the above data. 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.
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). 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.
Solutions to MC 1. ANS:C2.ANS:D3.ANS:D4.ANS:C5.ANS:C6.ANS:C7.ANS:D8.ANS:A9. ANS:D10.ANS:D 11. ANS: C12.ANS:D13.ANS: C14.ANS:D15.ANS: D16.ANS:B17.ANS: C18. ANS: B 19. ANS: C20.ANS:C21.ANS: B22.ANS:C23.ANS: D24.ANS:C25.ANS: C26. ANS: A 27. ANS: B28. ANS: D29. ANS: CSolutions to Short Answer 1. ANS:
a. -47 (rounded). Since the covariance is negative, it indicates a negative relationship between x and y. b. -0.922. There is a strong negative relationship between x and y.
2. ANS:
a. 0.0322 b. 0.0322
c. minimum = $16.24 maximum = $39.06 d. 2,000
3. ANS:
a.
= 24.112 + 0.816x b.
If x = 50 then = 24.112 + 0.816x ? 24.1 + 0.82 ( 50 ) = 65.1
c. 0.675 So there is a fairly strong positive relationship between x and y.
Practice Test 2 Business Statistics:
Multiple Choice: Each is worth two points
Identify the letter of the choice that best completes the statement or answers the question. ____ 1. The sample statistic s is the point estimator of
a. ? b. ? c. d.
____ 2. A sample statistic is an unbiased estimator of the population parameter if
a. the expected value of the sample statistic is equal to zero
b. the expected value of the sample statistic is equal to one
c. the expected value of the sample statistic is equal to the population parameter d. it is equal to zero
____
3. A property of a point estimator that occurs whenever larger sample sizes tend to provide point estimates closer to the population
parameter is known as a. efficiency
b. unbiased sampling c. consistency d. relative estimation
____
4. A random sample of 121 bottles of cologne showed an average content of 4 ounces. It is known that the standard deviation of the contents (i.e., of the population) is 0.22 ounces. In this problem the 0.22 is a. a parameter
b. a statistic
c. the standard error of the mean
d. the average content of colognes in the long run
____
5. A sample of 92 observations is taken from an infinite population. The sampling distribution of is approximately
a. normal because is always approximately normally distributed
b. normal because the sample size is small in comparison to the population size c. normal because of the central limit theorem
d. None of these alternatives is correct.
____
6. As the number of degrees of freedom for a t distribution increases, the difference between the t distribution and the standard normal
distribution
a. becomes larger
b. becomes smaller c. stays the same
____
d. None of these alternatives is correct.
7. From a population of 200 elements, a sample of 49 elements is selected. It is determined that the sample mean is 56 and the sample
standard deviation is 14. The standard error of the mean is a. 3 b. 2
c. greater than 2 d. less than 2
____
8. Which of the following is(are) point estimator(s)?
a. ? b. ?
c. s d. ?
____
9. A population characteristic, such as a population mean, is called
a. a statistic
b. a parameter c. a sample
d. the mean deviation
____
10. The sample statistic, such as , s, or , that provides the point estimate of the population parameter is known as
a. a point estimator
b. a parameter
c. a population parameter d. a population statistic
____
11. The fact that the sampling distribution of sample means can be approximated by a normal probability distribution whenever the
sample size is large is based on the a. central limit theorem
b. fact that we have tables of areas for the normal distribution
c. assumption that the population has a normal distribution d. None of these alternatives is correct.
____
12. Random samples of size 17 are taken from a population that has 200 elements, a mean of 36, and a standard deviation of 8. The
mean and the standard deviation of the sampling distribution of the sample means are a. 8.7 and 1.94
b. 36 and 1.94 c. 36 and 1.86