Statistics and Economics

Exhibit 9-5 n = 16 H0: m ≥ 80 nar005-1.jpg = 75.607 Ha: m < 80 s = 8.246 Assume population is normally distributed. Refer to Exhibit 9-5. The test statistic equals

-2.131

Exhibit 10-5 The following information was obtained from matched samples. Individual Method 1 Method 2 1 7 5 2 5 9 3 6 8 4 7 7 5 5 6 Refer to Exhibit 10-5. The 95% confidence interval for the difference between the two population means is

-3.776 to 1.776

Exhibit 10-4 The following information was obtained from independent random samples. Assume normally distributed populations with equal variances. Sample 1 Sample 2 Sample Mean 45 42 Sample Variance 85 90 Sample Size 10 12 Refer to Exhibit 10-4. The 95% confidence interval for the difference between the two population means is

-5.372 to 11.372

Exhibit 5-10 The probability that Pete will catch fish on a particular day when he goes fishing is 0.8. Pete is going fishing 3 days next week. Refer to Exhibit 5-10. The variance of the number of days Pete will catch fish is

.48

The sample size that guarantees all estimates of proportions will meet the margin of error requirements is computed using a planning value of p equal to

.50

Exhibit 5-7 A 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

.96

If the data distribution is symmetric, the skewness is

0

Exhibit 10-8 In order to determine whether or not there is a significant difference between the hourly wages of two companies, the following data have been accumulated. Company A Company B Sample size 80 60 Sample mean $16.75 $16.25 Population standard deviation $1.00 $0.95 Refer to Exhibit 10-8. The p-value is

0.0026

X is a normally distributed random variable with a mean of 5 and a variance of 4. The probability that x is greater than 10.52 is

0.0029

X is a normally distributed random variable with a mean of 22 and a standard deviation of 5. The probability that x is less than 9.7 is

0.0069

Exhibit 9-1 n = 36 H0: m ≤ 20 nar001-1.jpg = 24.6 Ha: m > 20 s = 12 Refer to Exhibit 9-1. The p-value is

0.0107

Exhibit 9-5 n = 16 H0: m ≥ 80 nar005-1.jpg = 75.607 Ha: m < 80 s = 8.246 Assume population is normally distributed. Refer to Exhibit 9-5. The p-value is equal to

0.0166

Exhibit 7-4 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. Refer to Exhibit 7-4. The standard error of the mean equals

0.0200

Random samples of size 525 are taken from a process (an infinite population) whose population proportion is 0.3. The standard deviation of the sample proportions (i.e., the standard error of the proportion) is

0.0200

Exhibit 9-2 The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took the customers in the sample to check out was 3.1 minutes. The population standard deviation is known to be 0.5 minutes. We want to test to determine whether or not the mean waiting time of all customers is significantly more than 3 minutes. Refer to Exhibit 9-2. The p-value is

0.0228

Exhibit 5-8 The student body of a large university consists of 60% female students. A random sample of 8 students is selected. Refer to Exhibit 5-8. What is the probability that among the students in the sample exactly two are female?

0.0413

Exhibit 6-5 The weight of items produced by a machine is normally distributed with a mean of 8 ounces and a standard deviation of 2 ounces. Refer to Exhibit 6-5. What is the probability that a randomly selected item will weigh between 11 and 12 ounces?

0.0440

Exhibit 2-1 The numbers of hours worked (per week) by 400 statistics students are shown below. Number of hours Frequency 0 - 9 20 10 - 19 80 20 - 29 200 30 - 39 100 Refer to Exhibit 2-1. The relative frequency of students working 9 hours or less

0.05

if A and B are independent events with p(a)= 0.05 and P(B)=0.65 then P(A|B)=

0.05

Exhibit 6-4 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. Refer to Exhibit 6-4. What is the probability that a randomly selected individual with an MBA degree will get a starting salary of at least $47,500?

0.0668

Exhibit 6-6 The life expectancy of a particular brand of tire is normally distributed with a mean of 40,000 and a standard deviation of 5,000 miles. Refer to Exhibit 6-6. What is the probability that a randomly selected tire will have a life of at least 47,500 miles?

0.0668

In a regression analysis if SSE = 500 and SSR = 300, then the coefficient of determination is

0.3750

Exhibit 6-5 The weight of items produced by a machine is normally distributed with a mean of 8 ounces and a standard deviation of 2 ounces. Refer to Exhibit 6-5. What percentage of items will weigh between 6.4 and 8.9 ounces?

0.4617

Exhibit 10-8 In order to determine whether or not there is a significant difference between the hourly wages of two companies, the following data have been accumulated. Company A Company B Sample size 80 60 Sample mean $16.75 $16.25 Population standard deviation $1.00 $0.95 Refer to Exhibit 10-8. A point estimate for the difference between the two sample means is

0.50

Of the last 100 customers entering a computer shop, 25 have purchased a computer. If the classical method for computing probability is used, the probability that the next customer will purchase a computer is

0.50

If a data set has SST = 2,000 and SSE = 800, then the coefficient of determination is

0.6

Exhibit 6-2 The travel time for a college student traveling between her home and her college is uniformly distributed between 40 and 90 minutes. Refer to Exhibit 6-2. The probability that her trip will take longer than 60 minutes is

0.600

In a regression analysis if SSE = 200 and SSR = 300, then the coefficient of determination is

0.6000

Exhibit 12-4 The following information regarding a dependent variable (Y) and an independent variable (X) is provided. Y X 4 2 3 1 4 4 6 3 8 5 SSE = 6 SST = 16 Refer to Exhibit 12-4. The coefficient of determination is

0.625

if P(A)= 0.38, P(B)= 0.83 and P(A under B)= 0.57 then P(AUB)=

0.64

In a regression analysis if SST = 4500 and SSE = 1575, then the coefficient of determination is

0.65

Exhibit 5-1 The following represents the probability distribution for the daily demand of microcomputers at a local store. Demand Probability 0 0.1 1 0.2 2 0.3 3 0.2 4 0.2 Refer to Exhibit 5-1. The probability of having a demand for at least two microcomputers is

0.7

Exhibit 12-4 The following information regarding a dependent variable (Y) and an independent variable (X) is provided. Y X 4 2 3 1 4 4 6 3 8 5 SSE = 6 SST = 16 Refer to Exhibit 12-4. The coefficient of correlation is

0.7906

Exhibit 6-2 The travel time for a college student traveling between her home and her college is uniformly distributed between 40 and 90 minutes. Refer to Exhibit 6-2. The probability that she will finish her trip in 80 minutes or less is

0.8

If an interval estimate is said to be constructed at the 90% confidence level, the confidence coefficient would be

0.9

Exhibit 5-2 The probability distribution for the daily sales at Michael's Co. is given below. Daily Sales ($1,000s) Probability 40 0.1 50 0.4 60 0.3 70 0.2 Refer to Exhibit 5-2. The probability of having sales of at least $50,000 is

0.90

If we want to provide a 95% confidence interval for the mean of a population, the confidence coefficient is

0.95

Exhibit 6-4 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. Refer to Exhibit 6-4. What is the probability that a randomly selected individual with an MBA degree will get a starting salary of at least $30,000?

0.9772

Exhibit 2-1 The numbers of hours worked (per week) by 400 statistics students are shown below. Number of hours Frequency 0 - 9 20 10 - 19 80 20 - 29 200 30 - 39 100 Refer to Exhibit 2-1. The cumulative percent frequency for the class of 30 - 39 is

100%

Exhibit 12-4 The following information regarding a dependent variable (Y) and an independent variable (X) is provided. Y X 4 2 3 1 4 4 6 3 8 5 SSE = 6 SST = 16 Refer to Exhibit 12-4. The least squares estimate of the Y intercept is

2

Exhibit 9-2 The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took the customers in the sample to check out was 3.1 minutes. The population standard deviation is known to be 0.5 minutes. We want to test to determine whether or not the mean waiting time of all customers is significantly more than 3 minutes. Refer to Exhibit 9-2. The test statistic is

2.00

Exhibit 9-4 A random sample of 16 students selected from the student body of a large university had an average age of 25 years. We want to determine if the average age of all the students at the university is significantly different from 24. Assume the distribution of the population of ages is normal with a standard deviation of 2 years. Refer to Exhibit 9-4. The test statistic is

2.00

Exhibit 5-5 AMR is a computer-consulting firm. The number of new clients that they have obtained each month has ranged from 0 to 6. The number of new clients has the probability distribution that is shown below. Number of New Clients Probability 0 0.05 1 0.10 2 0.15 3 0.35 4 0.20 5 0.10 6 0.05 Refer to Exhibit 5-5. The variance is

2.0475

The t value with a 95% confidence and 24 degrees of freedom is

2.064

Exhibit 12-3 Regression analysis was applied between sales data (in $1,000s) and advertising data (in $100s) and the following information was obtained. nar003-1.jpg = 12 + 1.8x n = 17 SSR = 225 SSE = 75 sb1 = 0.2683 Refer to Exhibit 12-3. Using a = 0.05, the critical t value for testing the significance of the slope is

2.131

Exhibit 5-1 The following represents the probability distribution for the daily demand of microcomputers at a local store. Demand Probability 0 0.1 1 0.2 2 0.3 3 0.2 4 0.2 Refer to Exhibit 5-1. The expected daily demand is

2.2

The z value for a 97.8% confidence interval estimation is

2.29

Exhibit 9-1 n = 36 H0: m ≤ 20 nar001-1.jpg = 24.6 Ha: m > 20 s = 12 Refer to Exhibit 9-1. The test statistic equals

2.3

Exhibit 5-10 The probability that Pete will catch fish on a particular day when he goes fishing is 0.8. Pete is going fishing 3 days next week. Refer to Exhibit 5-10. The expected number of days Pete will catch fish is

2.4

Exhibit 10-13 Part of an ANOVA table is shown below. ANOVA Source of Variation DF SS MS F Between Treatments 3 180 Within Treatments (Error) Total 18 480 Refer to Exhibit 10-13. The mean square within treatments (MSE) is

20

Random samples of size 36 are taken from a process (an infinite population) whose mean and standard deviation are 20 and 15, respectively. The distribution of the population is unknown. The mean and the standard error of the distribution of sample mean are

20 and 2.5

Exhibit 2-1 The numbers of hours worked (per week) by 400 statistics students are shown below. Number of hours Frequency 0 - 9 20 10 - 19 80 20 - 29 200 30 - 39 100 Refer to Exhibit 2-1. The percentage of students working 10 - 19 hours is

20%

Random samples of size 81 are taken from a process (an infinite population) whose mean and standard deviation are 200 and 18, respectively. The distribution of the population is unknown. The mean and the standard error of the distribution of sample means are

200 and 2

Exhibit 6-4 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. Refer to Exhibit 6-4. What percentage of MBA's will have starting salaries of $34,000 to $46,000?

76.98%

Exhibit 6-6 The life expectancy of a particular brand of tire is normally distributed with a mean of 40,000 and a standard deviation of 5,000 miles. Refer to Exhibit 6-6. What percentage of tires will have a life of 34,000 to 46,000 miles?

76.98%

Exhibit 3-1 A researcher has collected the following sample data. 5 12 6 8 5 6 7 5 12 4 Refer to Exhibit 3-1. The 75th percentile is

8

The assembly time for a product is uniformly distributed between 6 to 10 minutes. The expected assembly time (in minutes) is

8

Exhibit 5-6 Probability Distribution x f(x) 10 .2 20 .3 30 .4 40 .1 Refer to Exhibit 5-6. The variance of x equals

84

Exhibit 11-5 Last school year, the student body of a local university consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors. A sample of 300 students taken from this year's student body showed the following number of students in each classification. Freshmen 83 Sophomores 68 Juniors 85 Seniors 64 We are interested in determining whether or not there has been a significant change in the classifications between the last school year and this school year. Refer to Exhibit 11-5. The expected number of freshmen is

90

Exhibit 7-4 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. Refer to Exhibit 7-4. In this problem the 0.22 is

A parameter

Exhibit 9-1 n = 36 H0: m ≤ 20 nar001-1.jpg = 24.6 Ha: m > 20 s = 12 Refer to Exhibit 9-1. If the test is done at a .05 level of significance, the null hypothesis should

Be rejected

Exhibit 8-3 A random sample of 81 automobiles traveling on a section of an interstate showed an average speed of 60 mph. The distribution of speeds of all cars on this section of highway is normally distributed, with a standard deviation of 13.5 mph. Refer to Exhibit 8-3. If the sample size was 25 (other factors remain unchanged), the interval for m would

Become wider

A Scanner Data User Survey of 50 companies found that the average amount spent on scanner data per category of consumer goods was $387,325 (Mercer Management Consulting, Inc., April 24, 1997). The $387,325 is an example of

Both quantitative data and a descriptive statistic are correct

The test statistic F is the ratio

MSTR/MSE

A simple random sample of 28 observations was taken from a large population. The sample mean equaled 50. Fifty is a

Point estimate

In a residual plot against x that does not suggest we should challenge the assumptions of our regression model, we would expect to see

a horizontal band of points centered near zero

The probability that the interval estimation procedure will generate an interval that does not contain the actual value of the population parameter being estimated is the

confidence coefficient

The ability of an interval estimate to contain the value of the population parameter is described by the

confidence level

A numerical measure of linear association between two variables is the

correlation coefficient

Since the population is always larger than the sample, the value of the sample mean

could be larger, equal to, or smaller than the true value of the population mean

The average age in a sample of 90 students at City College is 20. As a result of this sample, it can be concluded that the average age of all the students at City College

could be larger, smaller, or equal to 20

the sample varience

could be smaller, equal to, or larger than the true value of the population variance

A numerical measure of linear association between two variables is the

covariance

A histogram is not appropriate for displaying which of the following types of information?

cumulative frequency

As the sample size increases, the margin of error

decreases

The t distribution is a family of similar probability distributions, with each individual distribution depending on a parameter known as the

degrees of freedom

Exhibit 1-2 In a sample of 3,200 registered voters, 1,440, or 45%, approve of the way the President is doing his job. Refer to Exhibit 1-2. The 45% approval is an example of

descriptive statistics

The owner of a factory regularly requests a graphical summary of all employees' salaries. The graphical summary of salaries is an example of

descriptive statistics

The summaries of data, which may be tabular, graphical, or numerical, are referred to as

descriptive statistics

Exhibit 2-1 The numbers of hours worked (per week) by 400 statistics students are shown below. Number of hours Frequency 0 - 9 20 10 - 19 80 20 - 29 200 30 - 39 100 Refer to Exhibit 2-1. The cumulative frequency for the class of 20 - 29

is 300

All of the following are true about the standard error of the mean except

it is larger than the standard deviation of the population

If a hypothesis is rejected at 95% confidence,

it must also be rejected at the 90% confidence

In testing for the equality of k population means, the number of treatments is

k

Exhibit 11-4 When individuals in a sample of 150 were asked whether or not they supported capital punishment, the following information was obtained. Do you support Number of capital punishment? individuals Yes 40 No 60 No Opinion 50 We are interested in determining whether or not the opinions of the individuals (as to Yes, No, and No Opinion) are uniformly distributed. Refer to Exhibit 11-4. The p-value is

larger than 0.1

Exhibit 9-3 n = 49 H0: m = 50 nar003-1.jpg = 54.8 Ha: m ≠ 50 s = 28 Refer to Exhibit 9-3. The p-value is equal to

0.2302

Exhibit 5-2 The probability distribution for the daily sales at Michael's Co. is given below. Daily Sales ($1,000s) Probability 40 0.1 50 0.4 60 0.3 70 0.2 Refer to Exhibit 5-2. The expected daily sales are

$56,000

Regression analysis was applied between sales data (in $1,000s) and advertising data (in $100s) and the following information was obtained. nar003-1.jpg = 12 + 1.8x n = 17 SSR = 225 SSE = 75 sb1 = 0.2683 Refer to Exhibit 12-3. Based on the above estimated regression equation, if advertising is $3,000, then the point estimate for sales (in dollars) is

$66,000

Regression analysis was applied between sales (in $1,000) and advertising (in $100), and the following regression function was obtained. mc018-1.jpg = 80 + 6.2x Based on the above estimated regression line, if advertising is $10,000, then the point estimate for sales (in dollars) is

$700,000

Regression analysis was applied between sales (in $1000) and advertising (in $100) and the following regression function was obtained. mc019-1.jpg = 500 + 4x Based on the above estimated regression line if advertising is $10,000, then the point estimate for sales (in dollars) is

$900,000

Exhibit 12-6 You are given the following information about y and x. y Dependent Variable x Independent Variable 12 4 3 6 7 2 6 4 Refer to Exhibit 12-6. The sample correlation coefficient equals

-0.4364

Exhibit 10-5 The following information was obtained from matched samples. Individual Method 1 Method 2 1 7 5 2 5 9 3 6 8 4 7 7 5 5 6 Refer to Exhibit 10-5. The null hypothesis tested is H0: md = 0. The test statistic for the difference between the two population means is

-1

Exhibit 10-5 The following information was obtained from matched samples. Individual Method 1 Method 2 1 7 5 2 5 9 3 6 8 4 7 7 5 5 6 Refer to Exhibit 10-5. The point estimate for the difference between the means of the two populations (method 1 - method 2) is

-1

Exhibit 12-6 You are given the following information about y and x. y Dependent Variable x Independent Variable 12 4 3 6 7 2 6 4 Refer to Exhibit 12-6. The least squares estimate of b1 equals

-1

Read the t statistic from the table of t distributions and circle the correct answer. A one-tailed test (lower tail), a sample size of 10 at a .10 level of significance; t =

-1.383

Read the z statistics from the normal distribution table and circle the correct answer. A two-tailed test at a .0694 level of significance; z =

-1.48 and 1.48

Read the z statistic from the normal distribution table and circle the correct answer. A one-tailed test (lower tail) at a .063 level of significance; z =

-1.53

Z is a standard normal random variable. What is the value of z if the area to the right of z is 0.9803?

-2.06

Exhibit 5-11 The random variable x is the number of occurrences of an event over an interval of ten minutes. It can be assumed that the probability of an occurrence is the same in any two time periods of an equal length. It is known that the mean number of occurrences in ten minutes is 5.3. Refer to Exhibit 5-11. The probability that there are less than 3 occurrences is

.1016

Exhibit 5-10 The probability that Pete will catch fish on a particular day when he goes fishing is 0.8. Pete is going fishing 3 days next week. Refer to Exhibit 5-10. The probability that Pete will catch fish on one day or less is

.104

if P(A)= 0.62, P(B)= 0.47 and P(A U B)= .88 then P(A under B)=

.2100

Exhibit 12-4 The following information regarding a dependent variable (Y) and an independent variable (X) is provided. Y X 4 2 3 1 4 4 6 3 8 5 SSE = 6 SST = 16 Refer to Exhibit 12-4. The MSE is

2

Exhibit 5-11 The random variable x is the number of occurrences of an event over an interval of ten minutes. It can be assumed that the probability of an occurrence is the same in any two time periods of an equal length. It is known that the mean number of occurrences in ten minutes is 5.3. Refer to Exhibit 5-11. The probability that there are 8 occurrences in ten minutes is

0.0771

Exhibit 5-10 The probability that Pete will catch fish on a particular day when he goes fishing is 0.8. Pete is going fishing 3 days next week. Refer to Exhibit 5-10. The probability that Pete will catch fish on exactly one day is

0.096

An experiment consists of four outcomes with P(E1) = 0.2, P(E2) = 0.3, and P(E3) = 0.4. The probability of outcome E4 is

0.100

Exhibit 9-6 A random sample of 100 people was taken. Eighty of the people in the sample favored Candidate A. We are interested in determining whether or not the proportion of the population in favor of Candidate A is significantly more than 75%. Refer to Exhibit 9-6. The p-value is

0.1056

Exhibit 6-5 The weight of items produced by a machine is normally distributed with a mean of 8 ounces and a standard deviation of 2 ounces. Refer to Exhibit 6-5. What is the probability that a randomly selected item will weigh more than 10 ounces?

0.1587

Exhibit 12-6 You are given the following information about y and x. y Dependent Variable x Independent Variable 12 4 3 6 7 2 6 4 Refer to Exhibit 12-6. The coefficient of determination equals

0.1905

Exhibit 12-4 The following information regarding a dependent variable (Y) and an independent variable (X) is provided. Y X 4 2 3 1 4 4 6 3 8 5 SSE = 6 SST = 16 Refer to Exhibit 12-4. The least squares estimate of the slope is

1

If all the points of a scatter diagram lie on the least squares regression line, then the coefficient of determination for these variables based on this data is

1

A lottery is conducted using three urns. Each urn contains chips numbered from 0 to 9. One chip is selected at random from each urn. The total number of sample points in the sample space is

1,000

Read the z statistic from the normal distribution table and circle the correct answer. A one-tailed test (upper tail) at a .123 level of significance; z =

1.16

Exhibit 5-7 A 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

1.2

Exhibit 9-3 n = 49 H0: m = 50 nar003-1.jpg = 54.8 Ha: m ≠ 50 s = 28 Refer to Exhibit 9-3. The test statistic equals

1.2

Exhibit 9-6 A random sample of 100 people was taken. Eighty of the people in the sample favored Candidate A. We are interested in determining whether or not the proportion of the population in favor of Candidate A is significantly more than 75%. Refer to Exhibit 9-6. The test statistic is

1.25

Read the t statistic from the table of t distributions and circle the correct answer. A two-tailed test, a sample of 20 at a .20 level of significance; t =

1.328

Exhibit 7-3 The 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 population standard deviation is

1.414

Exhibit 5-5 AMR is a computer-consulting firm. The number of new clients that they have obtained each month has ranged from 0 to 6. The number of new clients has the probability distribution that is shown below. Number of New Clients Probability 0 0.05 1 0.10 2 0.15 3 0.35 4 0.20 5 0.10 6 0.05 Refer to Exhibit 5-5. The standard deviation is

1.431

From a population of 500 elements, a sample of 225 elements is selected. It is known that the variance of the population is 900. The standard error of the mean is approximately

1.4847

Exhibit 8-3 A random sample of 81 automobiles traveling on a section of an interstate showed an average speed of 60 mph. The distribution of speeds of all cars on this section of highway is normally distributed, with a standard deviation of 13.5 mph. Refer to Exhibit 8-3. The value to use for the standard error of the mean is

1.5

Exhibit 8-3 A random sample of 81 automobiles traveling on a section of an interstate showed an average speed of 60 mph. The distribution of speeds of all cars on this section of highway is normally distributed, with a standard deviation of 13.5 mph. Refer to Exhibit 8-3. If we are interested in determining an interval estimate for m at 86.9% confidence, the z value to use is

1.51

Exhibit 11-5 Last school year, the student body of a local university consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors. A sample of 300 students taken from this year's student body showed the following number of students in each classification. Freshmen 83 Sophomores 68 Juniors 85 Seniors 64 We are interested in determining whether or not there has been a significant change in the classifications between the last school year and this school year. Refer to Exhibit 11-5. The calculated value for the test statistic equals

1.6615

Exhibit 5-4 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 Refer to Exhibit 5-4. The expected number of machine breakdowns per month is

1.70

Read the t statistic from the table of t distributions and circle the correct answer. A one-tailed test (upper tail), a sample size of 18 at a .05 level of significance t =

1.740

Exhibit 11-7 In the past, 35% of the students at ABC University were in the Business College, 35% of the students were in the Liberal Arts College, and 30% of the students were in the Education College. To see whether or not the proportions have changed, a sample of 300 students was taken. Ninety of the sample students are in the Business College, 120 are in the Liberal Arts College, and 90 are in the Education College. Refer to Exhibit 11-7. The expected frequency for the Business College is

105

Exhibit 12-6 You are given the following information about y and x. y Dependent Variable x Independent Variable 12 4 3 6 7 2 6 4 Refer to Exhibit 12-6. The least squares estimate of b0 equals

11

The weights (in pounds) of a sample of 36 individuals were recorded and the following statistics were calculated mean = 160 range = 60 mode = 165 variance = 324 median = 170 The coefficient of variation equals

11.25%

How many different samples of size 3 (without replacement) can be taken from a finite population of size 10?

120

A simple random sample of 64 observations was taken from a large population. The population standard deviation is 120. The sample mean was determined to be 320. The standard error of the mean is

15

There are 6 children in a family. The number of children defines a population. The number of simple random samples of size 2 (without replacement) which are possible equals

15

Exhibit 11-8 The table below gives beverage preferences for random samples of teens and adults. Teens Adults Total Coffee 50 200 250 Tea 100 150 250 Soft Drink 200 200 400 Other 50 50 100 400 600 1,000 We are asked to test for independence between age (i.e., adult and teen) and drink preferences. Refer to Exhibit 11-8. The expected number of adults who prefer coffee is

150

A simple random sample of 5 observations from a population containing 400 elements was taken, and the following values were obtained. 12 18 19 20 21 A point estimate of the population mean is

18

Exhibit 7-3 The 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

18.0

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

180 and 1.74

Exhibit 10-4 The following information was obtained from independent random samples. Assume normally distributed populations with equal variances. Sample 1 Sample 2 Sample Mean 45 42 Sample Variance 85 90 Sample Size 10 12 Refer to Exhibit 10-4. The degrees of freedom for the t distribution are

19

Exhibit 11-4 When individuals in a sample of 150 were asked whether or not they supported capital punishment, the following information was obtained. Do you support Number of capital punishment? individuals Yes 40 No 60 No Opinion 50 We are interested in determining whether or not the opinions of the individuals (as to Yes, No, and No Opinion) are uniformly distributed. Refer to Exhibit 11-4. The number of degrees of freedom associated with this problem is

2

Exhibit 5-6 Probability Distribution x f(x) 10 .2 20 .3 30 .4 40 .1 Refer to Exhibit 5-6. The expected value of x equals

24

Exhibit 6-1 Consider the continuous random variable x, which has a uniform distribution over the interval from 20 to 28. Refer to Exhibit 6-1. The mean of x is

24

Exhibit 2-1 The numbers of hours worked (per week) by 400 statistics students are shown below. Number of hours Frequency 0 - 9 20 10 - 19 80 20 - 29 200 30 - 39 100 Refer to Exhibit 2-1. The percentage of students working 19 hours or less is

25%

Exhibit 2-4 A survey of 400 college seniors resulted in the following crosstabulation regarding their undergraduate major and whether or not they plan to go to graduate school. Undergraduate Major Graduate School Business Engineering Others Total Yes 35 42 63 140 No 91 104 65 260 Total 126 146 128 400 Refer to Exhibit 2-4. Of those students who are majoring in business, what percentage plans to go to graduate school?

27.78

Exhibit 10-13 Part of an ANOVA table is shown below. ANOVA Source of Variation DF SS MS F Between Treatments 3 180 Within Treatments (Error) Total 18 480 Refer to Exhibit 10-13. The test statistic is

3

Exhibit 10-4 The following information was obtained from independent random samples. Assume normally distributed populations with equal variances. Sample 1 Sample 2 Sample Mean 45 42 Sample Variance 85 90 Sample Size 10 12 Refer to Exhibit 10-4. The point estimate for the difference between the means of the two populations is

3

Exhibit 10-8 In order to determine whether or not there is a significant difference between the hourly wages of two companies, the following data have been accumulated. Company A Company B Sample size 80 60 Sample mean $16.75 $16.25 Population standard deviation $1.00 $0.95 Refer to Exhibit 10-8. The test statistic is

3.01

Exhibit 5-5 AMR is a computer-consulting firm. The number of new clients that they have obtained each month has ranged from 0 to 6. The number of new clients has the probability distribution that is shown below. Number of New Clients Probability 0 0.05 1 0.10 2 0.15 3 0.35 4 0.20 5 0.10 6 0.05 Refer to Exhibit 5-5. The expected number of new clients per month is

3.05

Exhibit 6-5 The weight of items produced by a machine is normally distributed with a mean of 8 ounces and a standard deviation of 2 ounces. Refer to Exhibit 6-5. What percentage of items will weigh at least 11.7 ounces?

3.22%

Exhibit 2-1 The numbers of hours worked (per week) by 400 statistics students are shown below. Number of hours Frequency 0 - 9 20 10 - 19 80 20 - 29 200 30 - 39 100 Refer to Exhibit 2-1. The midpoint of the last class is

34.5

Exhibit 5-11 The random variable x is the number of occurrences of an event over an interval of ten minutes. It can be assumed that the probability of an occurrence is the same in any two time periods of an equal length. It is known that the mean number of occurrences in ten minutes is 5.3. Refer to Exhibit 5-11. The expected value of the random variable x is

5.3

Exhibit 7-5 Random samples of size 17 are taken from a population that has 200 elements, a mean of 36, and a standard deviation of 8. Refer to Exhibit 7-5. The mean and the standard deviation of the sampling distribution of the sample means are

36 ane 1.86

Exhibit 2-4 A survey of 400 college seniors resulted in the following crosstabulation regarding their undergraduate major and whether or not they plan to go to graduate school. Undergraduate Major Graduate School Business Engineering Others Total Yes 35 42 63 140 No 91 104 65 260 Total 126 146 128 400 Refer to Exhibit 2-4. What percentage of the students' undergraduate major is engineering?

36.5

Exhibit 11-4 When individuals in a sample of 150 were asked whether or not they supported capital punishment, the following information was obtained. Do you support Number of capital punishment? individuals Yes 40 No 60 No Opinion 50 We are interested in determining whether or not the opinions of the individuals (as to Yes, No, and No Opinion) are uniformly distributed. Refer to Exhibit 11-4. The calculated value for the test statistic equals

4

Exhibit 7-4 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. Refer to Exhibit 7-4. The point estimate of the mean content of all bottles is

4

The standard deviation of a sample of 100 observations equals 64. The variance of the sample equals

4,096

Exhibit 10-4 The following information was obtained from independent random samples. Assume normally distributed populations with equal variances. Sample 1 Sample 2 Sample Mean 45 42 Sample Variance 85 90 Sample Size 10 12 Refer to Exhibit 10-4. The standard error of mc051-1.jpg is

4.0

Exhibit 11-7 In the past, 35% of the students at ABC University were in the Business College, 35% of the students were in the Liberal Arts College, and 30% of the students were in the Education College. To see whether or not the proportions have changed, a sample of 300 students was taken. Ninety of the sample students are in the Business College, 120 are in the Liberal Arts College, and 90 are in the Education College. Refer to Exhibit 11-7. The calculated value for the test statistic equals

4.29

Exhibit 12-3 Regression analysis was applied between sales data (in $1,000s) and advertising data (in $100s) and the following information was obtained. nar003-1.jpg = 12 + 1.8x n = 17 SSR = 225 SSE = 75 sb1 = 0.2683 Refer to Exhibit 12-3. The critical F value at a = 0.05 is

4.54

Exhibit 12-3 Regression analysis was applied between sales data (in $1,000s) and advertising data (in $100s) and the following information was obtained. nar003-1.jpg = 12 + 1.8x n = 17 SSR = 225 SSE = 75 sb1 = 0.2683 Refer to Exhibit 12-3. The F statistic computed from the above data is

45

Exhibit 2-4 A survey of 400 college seniors resulted in the following crosstabulation regarding their undergraduate major and whether or not they plan to go to graduate school. Undergraduate Major Graduate School Business Engineering Others Total Yes 35 42 63 140 No 91 104 65 260 Total 126 146 128 400 Refer to Exhibit 2-4. Among the students who plan to go to graduate school, what percentage indicated "Other" majors?

45

Exhibit 3-1 A researcher has collected the following sample data. 5 12 6 8 5 6 7 5 12 4 Refer to Exhibit 3-1. The mode is

5

Exhibit 6-1 Consider the continuous random variable x, which has a uniform distribution over the interval from 20 to 28. Refer to Exhibit 6-1. The variance of x is approximately

5.333

Exhibit 11-7 In the past, 35% of the students at ABC University were in the Business College, 35% of the students were in the Liberal Arts College, and 30% of the students were in the Education College. To see whether or not the proportions have changed, a sample of 300 students was taken. Ninety of the sample students are in the Business College, 120 are in the Liberal Arts College, and 90 are in the Education College. Refer to Exhibit 11-7. The hypothesis is to be tested at the 5% level of significance. The critical value from the table equals

5.991

Exhibit 11-4 When individuals in a sample of 150 were asked whether or not they supported capital punishment, the following information was obtained. Do you support Number of capital punishment? individuals Yes 40 No 60 No Opinion 50 We are interested in determining whether or not the opinions of the individuals (as to Yes, No, and No Opinion) are uniformly distributed. Refer to Exhibit 11-4. The expected frequency for each group is

50

The median of a sample will always equal the

50th percentile

Exhibit 3-1 A researcher has collected the following sample data. 5 12 6 8 5 6 7 5 12 4 Refer to Exhibit 3-1. The median is

6

Exhibit 12-3 Regression analysis was applied between sales data (in $1,000s) and advertising data (in $100s) and the following information was obtained. nar003-1.jpg = 12 + 1.8x n = 17 SSR = 225 SSE = 75 sb1 = 0.2683 Refer to Exhibit 12-3. The t statistic for testing the significance of the slope is

6.709

Exhibit 10-13 Part of an ANOVA table is shown below. ANOVA Source of Variation DF SS MS F Between Treatments 3 180 Within Treatments (Error) Total 18 480 Refer to Exhibit 10-13. The mean square between treatments (MSTR) is

60

Exhibit 11-5 Last school year, the student body of a local university consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors. A sample of 300 students taken from this year's student body showed the following number of students in each classification. Freshmen 83 Sophomores 68 Juniors 85 Seniors 64 We are interested in determining whether or not there has been a significant change in the classifications between the last school year and this school year. Refer to Exhibit 11-5. The expected frequency of seniors is

60

Exhibit 11-8 The table below gives beverage preferences for random samples of teens and adults. Teens Adults Total Coffee 50 200 250 Tea 100 150 250 Soft Drink 200 200 400 Other 50 50 100 400 600 1,000 We are asked to test for independence between age (i.e., adult and teen) and drink preferences. Refer to Exhibit 11-8. The test statistic for this test of independence is

62.5

Exhibit 2-4 A survey of 400 college seniors resulted in the following crosstabulation regarding their undergraduate major and whether or not they plan to go to graduate school. Undergraduate Major Graduate School Business Engineering Others Total Yes 35 42 63 140 No 91 104 65 260 Total 126 146 128 400 Refer to Exhibit 2-4. What percentage of the students does not plan to go to graduate school?

65

Exhibit 3-1 A researcher has collected the following sample data. 5 12 6 8 5 6 7 5 12 4 Refer to Exhibit 3-1. The mean is

7

Exhibit 11-8 The table below gives beverage preferences for random samples of teens and adults. Teens Adults Total Coffee 50 200 250 Tea 100 150 250 Soft Drink 200 200 400 Other 50 50 100 400 600 1,000 We are asked to test for independence between age (i.e., adult and teen) and drink preferences. Refer to Exhibit 11-8. With a .05 level of significance, the critical value for the test is

7.815

It is known that the variance of a population equals 1,936. A random sample of 121 has been taken from the population. There is a .95 probability that the sample mean will provide a margin of error of

7.84 or less

Chapter 1

Chapter 10

Chapter 11

Chapter 12

Chapter 2

Chapter 3

Chapter 4

Chapter 6

Chapter 7

Chapter 8

Chapter 9

If A and B are independent events with P(A) = .1 and P(B) = .4, then

P(A ∩ B) = .04

The complement of P(A | B) is

P(AC | B)

A sample of five Fortune 500 companies showed the following industry codes: banking, banking, finance, retail, and banking. Based on this information, which of the following statements is correct?

Sixty percent of the sample of five companies are banking industries.

In determining the sample size necessary to estimate a population proportion, which of the following information is not needed?

The mean of the population

The error of rejecting a true null hypothesis is

a Type I error

An interval estimate is used to estimate

a population parameter

Positive values of covariance indicate

a positive relation between the x and the y variables

A portion of the population selected to represent the population is called

a sample

The most common type of observational study is

a survey

A frequency distribution is

a tabular summary of a set of data showing the number of items in each of several nonoverlapping classes

A graphical method of representing the sample points of a multiple-step experiment is

a tree diagram

If we are interested in testing whether the mean of population 1 is significantly larger than the mean of population 2, the

alternative hypothesis should state m1 - m2 > 0

Which of the following is not an example of descriptive statistics?

an estimate of the number of Alaska residents who have visited Canada

Any process that generates well-defined outcomes is

an experiment

Quantitative data

are always numeric

Categorical Data

are labels used to identify attributes of elements

Exhibit 8-3 A random sample of 81 automobiles traveling on a section of an interstate showed an average speed of 60 mph. The distribution of speeds of all cars on this section of highway is normally distributed, with a standard deviation of 13.5 mph. Refer to Exhibit 8-3. The 86.9% confidence interval for m is

b. 57.735 to 62.265

Categorical data can be graphically represented by using a(n)

bar chart

Using an a = 0.04, a confidence interval for a population proportion is determined to be 0.65 to 0.75. If the level of significance is decreased, the interval for the population proportion

becomes wider

Exhibit 10-13 Part of an ANOVA table is shown below. ANOVA Source of Variation DF SS MS F Between Treatments 3 180 Within Treatments (Error) Total 18 480 Refer to Exhibit 10-13. If at 95% confidence, we want to determine whether or not the means of the populations are equal, the p-value is

between 0.05 and 0.1

If two independent large samples are taken from two populations, the sampling distribution of the difference between the two sample means

can be approximated by a normal distribution

Since a sample is a subset of the population, the sample mean

can be larger, smaller, or equal to the mean of the population

If P(A) = 0.5 and P(B) = 0.5, then P(A ∩ B) is

cannot be determined from the information given

For ease of data entry into a university database, 1 denotes that the student is an undergraduate and 2 indicates that the student is a graduate student. In this case data are

categorical

A researcher is gathering data from four geographical areas designated: South = 1; North = 2; East = 3; West = 4. The designated geographical regions represent

categorical data

Data that provide labels or names for groupings of like items are known as

categorical data

In a post office, the mailboxes are numbered from 1 to 5,000. These numbers represent

categorical data

A theorem that allows us to use the normal probability distribution to approximate the sampling distribution of sample means and sample proportions whenever the sample size is large is known as the

central limit theorem

the mean of a sample is

computed by summing all the data values and dividing the sum by the number of items

Exhibit 11-4 When individuals in a sample of 150 were asked whether or not they supported capital punishment, the following information was obtained. Do you support Number of capital punishment? individuals Yes 40 No 60 No Opinion 50 We are interested in determining whether or not the opinions of the individuals (as to Yes, No, and No Opinion) are uniformly distributed. Refer to Exhibit 11-4. The conclusion of the test (at 95% confidence) is that the

distribution is uniform

A simple random sample from a process (an infinite population) is a sample selected such that

each element selected comes from the same population and each element is selected independently

In order to determine whether or not the means of two populations are equal,

either a t test or an analysis of variance can be performed

Statistical studies in which researchers control variables of interest are

experimental studies

If several frequency distributions are constructed from the same data set, the distribution with the widest class width will have the

fewest classes

Exhibit 11-5 Last school year, the student body of a local university consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors. A sample of 300 students taken from this year's student body showed the following number of students in each classification. Freshmen 83 Sophomores 68 Juniors 85 Seniors 64 We are interested in determining whether or not there has been a significant change in the classifications between the last school year and this school year. Refer to Exhibit 11-5. The p-value is

greater than 0.1

Exhibit 11-7 In the past, 35% of the students at ABC University were in the Business College, 35% of the students were in the Liberal Arts College, and 30% of the students were in the Education College. To see whether or not the proportions have changed, a sample of 300 students was taken. Ninety of the sample students are in the Business College, 120 are in the Liberal Arts College, and 90 are in the Education College. Refer to Exhibit 11-7. The p-value is

greater than 0.1

A common graphical presentation of quantitative data is a

histogram

In constructing a frequency distribution, as the number of classes are decreased, the class width

increases

It is impossible to construct a frame for a

infinite population

Exhibit 2-1 The numbers of hours worked (per week) by 400 statistics students are shown below. Number of hours Frequency 0 - 9 20 10 - 19 80 20 - 29 200 30 - 39 100 Refer to Exhibit 2-1. The cumulative relative frequency for the class of 20 - 29

is 0.75

Exhibit 2-1 The numbers of hours worked (per week) by 400 statistics students are shown below. Number of hours Frequency 0 - 9 20 10 - 19 80 20 - 29 200 30 - 39 100 Refer to Exhibit 2-1. The class width for this distribution

is 10

Exhibit 2-1 The numbers of hours worked (per week) by 400 statistics students are shown below. Number of hours Frequency 0 - 9 20 10 - 19 80 20 - 29 200 30 - 39 100 Refer to Exhibit 2-1. The number of students working 19 hours or less

is 100

Exhibit 11-8 The table below gives beverage preferences for random samples of teens and adults. Teens Adults Total Coffee 50 200 250 Tea 100 150 250 Soft Drink 200 200 400 Other 50 50 100 400 600 1,000 We are asked to test for independence between age (i.e., adult and teen) and drink preferences. Refer to Exhibit 11-8. The p-value is

less than 0.005

From a population of 200 elements, the standard deviation is known to be 14. A sample of 49 elements is selected. It is determined that the sample mean is 56. The standard error of the mean is

less than 2

When each data value in one sample is matched with a corresponding data value in another sample, the samples are known as

matched samples

The probability of the occurrence of event A in an experiment is 1/3. If the experiment is performed 2 times and event A did not occur, then on the third trial event A

may occur

Generally, which one of the following is the least appropriate measure of central tendency for a data set that contains outliers?

mean

The within-treatments estimate of s 2 is called the

mean square due to error

After the data has been arranged from smallest value to largest value, the value in the middle is called the

median

The 50th percentile is the

median

An important measure of location for categorical data is the

mode

A population where each element of the population is assigned to one and only one of several classes or categories is a

multinomial population

Exhibit 11-7 In the past, 35% of the students at ABC University were in the Business College, 35% of the students were in the Liberal Arts College, and 30% of the students were in the Education College. To see whether or not the proportions have changed, a sample of 300 students was taken. Ninety of the sample students are in the Business College, 120 are in the Liberal Arts College, and 90 are in the Education College. Refer to Exhibit 11-7. This problem is an example of a

multinomial population

Given that event E has a probability of 0.25, the probability of the complement of event E

must be 0.75

During a cold winter, the temperature stayed below zero for ten days (ranging from -20 to -5). The variance of the temperatures of the ten day period

must be at least 0

Events that have no sample points in common are

mutually exclusive events

For data skewed to the left, the skewness is

negative

Exhibit 5-4 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 Refer to Exhibit 5-4. The probability of at least 3 breakdowns in a month is