EC220 - Exam 2

The expected value of a random variable is the _____. Select one: a. median value b. mean value c. simple average of all the possible values d. most probable value

b. mean value

The following estimated regression model was developed relating yearly income (y in $1000s) of 30 individuals with their age (x1) and their gender (x2) (0 if male and 1 if female). ​ y^ = 30 + 0.7x1 + 3x2 ​ Also provided are SST = 1200 and SSE = 384. Refer to Exhibit 15-8. The yearly income of a 24-year-old male individual is _____. Select one: a. $46,800 b. $13.80 c. $49,800 d. $13,800

a. $46,800

Exhibit 15-8 The following estimated regression model was developed relating yearly income (y in $1000s) of 30 individuals with their age (x1) and their gender (x2) (0 if male and 1 if female). ​ y^= 30 + 0.7x1 + 3x2 ​ Also provided are SST = 1200 and SSE = 384. Refer to Exhibit 15-8. The multiple coefficient of determination is _____. Select one: a. .68 b. .42 c. .32 d. .50

a. .68

Exhibit 5-7A sample of 2,500 people was asked how many cups of coffee they drink in the morning. You are given the following sample information. Cups of Coffee ; Frequency 0 ; 700 1 ; 900 2 ; 600 3 ; 300 ; 2,500 Refer to Exhibit 5-7. The variance of the number of cups of coffee is _____. Select one: a. .96 b. 1 c. .9798 d. 2.4

a. .96

Exhibit 6-3The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds. Refer to Exhibit 6-3. The probability of a player weighing less than 250 pounds is _____. Select one: a. .9772 b. .0528 c. .4772 d. .5000

a. .9772

Assume z is a standard normal random variable. What is the value of z if the area between -z and zis .754? Select one: a. 1.16 b. .377 c. .123 d. 2.16

a. 1.16

Exhibit 7-3The following information was collected from a simple random sample of a population. 16 ; 19 ; 18 ; 17 ; 20 ; 18 Refer to Exhibit 7-3. The point estimate of the mean of the population is _____. Select one: a. 18.0 b. 16, since 16 is the smallest value in the sample c. 19.6 d. 108

a. 18.0

Exhibit 7-4A 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. Refer to Exhibit 7-4. In this problem, the .22 is _____. Select one: a. a parameter b. a statistic c. the standard error of the mean d. the average content of colognes in the long run

a. a parameter

As the sample size increases, the variability among the sample means _____. Select one: a. decreases b. depends upon the specific population being sampled c. increases d. remains the same

a. decreases

A marketing manager instructs his team to make 80 telephone calls to attempt to sell an insurance policy. The random variable in this experiment is the number of sales made. This random variable is a _____. Select one: a. discrete random variable b. complex random variable c. None of the answers is correct. d. continuous random variable

a. discrete random variable

A population has a mean of 80 and a standard deviation of 7. A sample of 49 observations will be taken. The probability that the mean from that sample will be larger than 82 is _____. Select one: a. .5228 b. .0228 c. .4772 d. .9772

b. .0228

Exhibit 6-3The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds. Refer to Exhibit 6-3. The probability of a player weighing more than 241.25 pounds is _____. Select one: a. .9010 b. .0495 c. .9505 d. .4505

b. .0495

A numerical measure of linear association between two variables is the _____. Select one: a. z-score b. correlation coefficient c. variance d. None of the answers is correct.

b. correlation coefficient

Exhibit 15-8 The following estimated regression model was developed relating yearly income (y in $1000s) of 30 individuals with their age (x1) and their term-3 gender (x2) (0 if male and 1 if female). ​ y^= 30 + 0.7x1 + 3x2 ​ Also provided are SST = 1200 and SSE = 384. Refer to Exhibit 15-8. From the above function, it can be said that the expected yearly income for _____. Select one: a. male is $3 more than females b. female is $3,000 more than males c. female is $3 more than males d. male is $3,000 more than females

b. female is $3,000 more than males

When the population has a normal distribution, the sampling distribution of is normally distributed _____. Select one: a. for any sample size of 50 or more b. for any sample size c. for any sample from a finite population d. for any sample size of 30 or more

b. for any sample size

A regression model between sales (y in $1000s), unit price (x1 in dollars) and television advertisement (x2 in dollars) resulted in the following function: ​ y^ = 7 - 3x1 + 5x2 ​ For this model, SSR = 3500, SSE = 1500, and the sample size is 18. Refer to Exhibit 15-2. The coefficient of x2 indicates that if television advertising is increased by $1 (holding the unit price constant), sales are expected to _____. Select one: a. decrease by $2000 b. increase by $5000 c. increase by $12,000 d. increase by $5

b. increase by $5000

Regression analysis is a statistical procedure for developing a mathematical equation that describes how _____. Select one: a. None of the answers is correct. b. one dependent and one or more independent variables are related c. one independent and one or more dependent variables are related d. several independent and several dependent variables are related

b. one dependent and one or more independent variables are related

Exhibit 5-7A sample of 2,500 people was asked how many cups of coffee they drink in the morning. You are given the following sample information. Cups of Coffee ; Frequency 0 ; 700 1 ; 900 2 ; 600 3 ; 300 ; 2,500 Refer to Exhibit 5-7. The expected number of cups of coffee is _____. Select one: a. 1.5 b. 1 c. 1.2 d. 1.7

c. 1.2

Exhibit 7-4A 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. Refer to Exhibit 7-4. The point estimate of the mean content of all bottles is _____. Select one: a. 121 b. .02 c. 4 d. .22

c. 4

Exhibit 7-4A 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. Refer to Exhibit 7-4. The standard error of the mean equals _____. Select one: a. .3636 b. 4.000 c. .0331 d. .0200

d. .0200

For any continuous random variable, the probability that the random variable takes on exactly a specific value is _____. Select one: a. 1 b. .50 c. any value between 0 and 1 d. 0

d. 0

Exhibit 6-3The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds. Refer to Exhibit 6-3. What is the minimum weight of the middle 95% of the players? Select one: a. None of the answers is correct. b. 196 c. 249 d. 151

d. 151

Random samples of size 49 are taken from a population that has 200 elements, a mean of 180, and a variance of 196. The distribution of the population is unknown. The mean and the standard error of the distribution of sample means are _____. Select one: a. 180 and 28 b. 180 and 1.74 c. 180 and 24.39 d. 180 and 2

d. 180 and 2

Exhibit 6-3The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds. Refer to Exhibit 6-3. What percent of players weigh between 180 and 220 pounds? Select one: a. 68.26% b. 34.13% c. 0.3413% d. None of the answers is correct

d. None of the answers is correct

Which of the following is NOT a characteristic of the normal probability distribution? Select one: a. The random variable assumes a value within plus or minus three standard deviations of its mean 99.72% of the time. b. The mean is equal to the median, which is also equal to the mode. c. The total area under the curve is always equal to 1. d. The graph of the curve is the shape of a rectangle.

d. The graph of the curve is the shape of a rectangle.

If r = 0.48 for data set A and r = -0.48 for data set B, which of the following is true? Select one: a. None of the answers is correct. b. The data values in A are all positive, while the data values in B are all negative. c. The variables in A are more strongly correlated than the variables in B. d. The two data sets have the same level of correlation.

d. The two data sets have the same level of correlation.

A regression model between sales (y in $1000s), unit price (x1 in dollars) and television advertisement (x2 in dollars) resulted in the following function: ​ y^ = 7 - 3x1 + 5x2 ​ For this model, SSR = 3500, SSE = 1500, and the sample size is 18. Refer to Exhibit 15-2. The coefficient of the unit price indicates that if the unit price is _____. Select one: a. decreased by $1 (holding advertising constant), sales are expected to decrease by $3 b. increased by $1 (holding advertising constant), sales are expected to increase by $3 c. increased by $1 (holding advertising constant), sales are expected to increase by $4000 d. increased by $1 (holding advertising constant), sales are expected to decrease by $3000

d. increased by $1 (holding advertising constant), sales are expected to decrease by $3000

If a qualitative variable has k levels, the number of dummy variables required is _____. Select one: a. k b. k + 1 c. 2k d. k− 1

d. k− 1

The difference between the observed value of the dependent variable and the value predicted by using the estimated regression equation is the _____. Select one: a. predicted interval b. standard error c. variance d. residual

d. residual

The probability distribution of all possible values of the sample mean is called the ____. Select one: a. random variation b. standard error c. central probability distribution d. sampling distribution of the sample mean

d. sampling distribution of the sample mean