Stats Final

As the goodness of fit for the estimated regression equation increases, the _____.

value of the coefficient of determination increases

In regression analysis, the independent variable is typically plotted on the _____.

x-axis of a scatter diagram

In the ANOVA, treatment refers to _____.

different levels of a factor

To determine whether the means of two populations are equal, _____.

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

A term that means the same as the term "variable" in an ANOVA procedure is _____.

factor

Regression analysis is a statistical procedure for developing a mathematical equation that describes how _____.

one dependent and one or more independent variables are related

A regression analysis between sales (y in $1000) and advertising (x in dollars) resulted in the following equation: = 50,000 + 6x ​ The above equation implies that an increase of _____.

$1 in advertising is associated with an increase of $6,000 in sales

Exhibit 13-3 To test whether or not there is a difference between treatments A, B, and C, a sample of 12 observations has been randomly assigned to the three treatments. You are given the results below. Treatment Observation A 20 30 25 33 B 22 26 20 28 C 40 30 28 22 ​ Refer to Exhibit 13-3. The test statistic to test the null hypothesis equals _____.

1.059

The critical F value with 6 numerator and 60 denominator degrees of freedom at α = .05 is _____.

2.25

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

The independent variable of interest in an ANOVA procedure is called _____.

a factor

The required condition for using an ANOVA procedure on data from several populations is that the _____.

sampled populations have equal variances

In a regression analysis, the variable that is used to predict the dependent variable ______.

is the independent variable

It is possible for the coefficient of determination to be _____.

less than 1

Exhibit 13-1 SSTR = 6,750 H0: μ1 = μ2 = μ3 = μ4 SSE = 8,000 Ha: At least one mean is different nT = 20 ​ ​ Refer to Exhibit 13-1. The null hypothesis _____.

should be rejected

Exhibit 13-7 The following is part of an ANOVA table, which was the result of three treatments and a total of 15 observations. Source of Variation Sum of Squares Degrees of Freedom Mean Square F Between treatments 64 Within treatments (Error) 96 Total ​ Refer to Exhibit 13-7. The number of degrees of freedom corresponding to between treatments is _____.

2

Exhibit 13-5 Part of an ANOVA table is shown below. Source of Variation Sum of Squares Degrees of Freedom Mean Square F Between treatments 180 3 Within treatments (Error) Total 480 18 ​ Refer to Exhibit 13-5. If at a 5% level of significance, we want to determine whether the means of the populations are equal, the critical value of F is _____.

3.29

An ANOVA procedure is applied to data obtained from 6 samples where each sample contains 20 observations. The degrees of freedom for the critical value of F are _____.

5 numerator and 114 denominator degrees of freedom

Exhibit 13-2 Source of Variation Sum of Squares Degrees of Freedom Mean Square F Between treatments 2,073.6 4 Between blocks 6,000.0 5 1,200 Error 20 288 Total 29 ​ Refer to Exhibit 13-2. The sum of squares due to error equals _____.

5,760

Exhibit 13-5 Part of an ANOVA table is shown below. Source of Variation Sum of Squares Degrees of Freedom Mean Square F Between treatments 180 3 Within treatments (Error) Total 480 18 ​ Refer to Exhibit 13-5. The mean square between treatments (MSTR) is _____.

60

When an analysis of variance is performed on samples drawn from k populations, the mean square between treatments (MSTR) is _____.

SSTR/(k - 1)

The difference between the observed value of the dependent variable and the value predicted by using the estimated regression equation is called _____.

a residual

Exhibit 10-9 Two major automobile manufacturers have produced compact cars with the same size engines. We are interested in determining whether or not there is a significant difference in the MPG (miles per gallon) of the two brands of automobiles. A random sample of eight cars from each manufacturer is selected, and eight drivers are selected to drive each automobile for a specified distance. The following data show the results of the test. Driver Manufacturer A Manufacturer B 1 32 28 2 27 22 3 26 27 4 26 24 5 25 24 6 29 25 7 31 28 8 25 27 Refer to Exhibit 10-9. At 90% confidence, the null hypothesis _____.

should be rejected

The equation that describes how the dependent variable (y) is related to the independent variable (x) is called _____.

the regression model

In an analysis of variance problem involving three treatments and 10 observations per treatment, SSE = 399.6. The MSE for this situation is _____.

14.8

Exhibit 13-6 Part of an ANOVA table is shown below. Source of Variation Sum of Squares Degrees of Freedom Mean Square F Between treatments 64 8 Within treatments (Error) 2 Total 100 ​ Refer to Exhibit 13-6. The mean square between treatments (MSTR) is _____.

16

Exhibit 10-9 Two major automobile manufacturers have produced compact cars with the same size engines. We are interested in determining whether or not there is a significant difference in the MPG (miles per gallon) of the two brands of automobiles. A random sample of eight cars from each manufacturer is selected, and eight drivers are selected to drive each automobile for a specified distance. The following data show the results of the test. Driver Manufacturer A Manufacturer B 1 32 28 2 27 22 3 26 27 4 26 24 5 25 24 6 29 25 7 31 28 8 25 27 Refer to Exhibit 10-9. The value of the test statistic is _____.

2.256

Exhibit 13-1 SSTR = 6,750 H0: μ1 = μ2 = μ3 = μ4 SSE = 8,000 Ha: At least one mean is different nT = 20 ​ ​ Refer to Exhibit 13-1. The test statistic to test the null hypothesis equals _____.

4.5

Exhibit 13-7 The following is part of an ANOVA table, which was the result of three treatments and a total of 15 observations. Source of Variation Sum of Squares Degrees of Freedom Mean Square F Between treatments 64 Within treatments (Error) 96 Total ​ Refer to Exhibit 13-7. If at a 5% level of significance, we want to determine whether or not the means of the populations are equal, the critical value of F is _____.

4.75

In an analysis of variance problem, if SST = 120 and SSTR = 80, then SSE is _____.

40

Exhibit 10-2 The following information was obtained from matched samples. The daily production rates for a random sample of workers before and after a training program are shown below. Worker Before After 1 20 22 2 25 23 3 27 27 4 23 20 5 22 25 6 20 19 7 17 18 Refer to Exhibit 10-2. Based on the results of the previous question, the _____.

null hypothesis should not be rejected

Exhibit 13-3 To test whether or not there is a difference between treatments A, B, and C, a sample of 12 observations has been randomly assigned to the three treatments. You are given the results below. Treatment Observation A 20 30 25 33 B 22 26 20 28 C 40 30 28 22 ​ Refer to Exhibit 13-3. The null hypothesis _____.

should not be rejected

In the analysis of variance procedure (ANOVA), factor refers to _____.

the independent variable

A regression analysis between sales (in $1000s) and price (in dollars) resulted in the following equation: ​ = 50,000 − 8x ​ The above equation implies that an increase of _____.

$1 in price is associated with a decrease of $8,000 in sales

Regression analysis was applied between sales (in $1000s) and advertising (in $100s), and the following regression function was obtained. ​ = 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 13-3 To test whether or not there is a difference between treatments A, B, and C, a sample of 12 observations has been randomly assigned to the three treatments. You are given the results below. Treatment Observation A 20 30 25 33 B 22 26 20 28 C 40 30 28 22 ​ Refer to Exhibit 13-3. The mean square between treatments (MSTR) equals _____.

36

Exhibit 13-1 SSTR = 6,750 H0: μ1 = μ2 = μ3 = μ4 SSE = 8,000 Ha: At least one mean is different nT = 20 ​ ​ Refer to Exhibit 13-1. The mean square within treatments (MSE) equals _____.

500

An experimental design where the experimental units are randomly assigned to the treatments is known as _____.

completely randomized design

Exhibit 13-5 Part of an ANOVA table is shown below. Source of Variation Sum of Squares Degrees of Freedom Mean Square F Between treatments 180 3 Within treatments (Error) Total 480 18 ​ Refer to Exhibit 13-5. The conclusion of the test is that the means _____.

may be equal

Exhibit 13-7 The following is part of an ANOVA table, which was the result of three treatments and a total of 15 observations. Source of Variation Sum of Squares Degrees of Freedom Mean Square F Between treatments 64 Within treatments (Error) 96 Total ​ Refer to Exhibit 13-7. The conclusion of the test is that the means _____.

may be equal

A least squares regression line ______.

may be used to predict a value of y if the corresponding x value is given

The least squares criterion is _____.

min E (yi - y^i)2

Exhibit 10-13 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 1 Company 2 n1 = 80 n2 = 60 1 = $10.80 2 = $10.00 σ1= $2.00 σ2= $1.50 Refer to Exhibit 10-13. The null hypothesis for this test is _____.

μ1 - μ2 = 0

Exhibit 13-3 To test whether or not there is a difference between treatments A, B, and C, a sample of 12 observations has been randomly assigned to the three treatments. You are given the results below. Treatment Observation A 20 30 25 33 B 22 26 20 28 C 40 30 28 22 ​ Refer to Exhibit 13-3. The null hypothesis for this ANOVA problem is _____.

μ1 = μ2 = μ3

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: μd = 0. The test statistic for the mean of the population of differences is _____.

-1

Exhibit 10-2 The following information was obtained from matched samples. The daily production rates for a random sample of workers before and after a training program are shown below. Worker Before After 1 20 22 2 25 23 3 27 27 4 23 20 5 22 25 6 20 19 7 17 18 Refer to Exhibit 10-2. The null hypothesis to be tested is H0: μd = 0. The value of the test statistic is _____.

0

Exhibit 10-2 The following information was obtained from matched samples. The daily production rates for a random sample of workers before and after a training program are shown below. Worker Before After 1 20 22 2 25 23 3 27 27 4 23 20 5 22 25 6 20 19 7 17 18 Refer to Exhibit 10-2. The point estimate for the mean of the population of difference is _____.

0

Exhibit 13-2 Source of Variation Sum of Squares Degrees of Freedom Mean Square F Between treatments 2,073.6 4 Between blocks 6,000.0 5 1,200 Error 20 288 Total 29 ​ Refer to Exhibit 13-2. The test statistic to test the null hypothesis equals _____.

1.8

Exhibit 10-9 Two major automobile manufacturers have produced compact cars with the same size engines. We are interested in determining whether or not there is a significant difference in the MPG (miles per gallon) of the two brands of automobiles. A random sample of eight cars from each manufacturer is selected, and eight drivers are selected to drive each automobile for a specified distance. The following data show the results of the test. Driver Manufacturer A Manufacturer B 1 32 28 2 27 22 3 26 27 4 26 24 5 25 24 6 29 25 7 31 28 8 25 27 Refer to Exhibit 10-9. The mean of the differences (Manufacturer A - Manufacturer B) is _____.

2.0

Exhibit 13-2 Source of Variation Sum of Squares Degrees of Freedom Mean Square F Between treatments 2,073.6 4 Between blocks 6,000.0 5 1,200 Error 20 288 Total 29 ​ Refer to Exhibit 13-2. The null hypothesis is to be tested at the 5% level of significance. The critical value from the table is _____.

2.87

Exhibit 13-6 Part of an ANOVA table is shown below. Source of Variation Sum of Squares Degrees of Freedom Mean Square F Between treatments 64 8 Within treatments (Error) 2 Total 100 ​ Refer to Exhibit 13-6. If at a 5% significance level we want to determine whether or not the means of the populations are equal, the critical value of F is _____. ​

2.93

Exhibit 13-7 The following is part of an ANOVA table, which was the result of three treatments and a total of 15 observations. Source of Variation Sum of Squares Degrees of Freedom Mean Square F Between treatments 64 Within treatments (Error) 96 Total ​ Refer to Exhibit 13-7. The mean square between treatments (MSTR) is _____.

32

Exhibit 13-7 The following is part of an ANOVA table, which was the result of three treatments and a total of 15 observations. Source of Variation Sum of Squares Degrees of Freedom Mean Square F Between treatments 64 Within treatments (Error) 96 Total ​ Refer to Exhibit 13-7. The computed test statistic is _____.

4

In a completely randomized design involving three treatments, the following information is provided: Treatment 1 Treatment 2 Treatment 3 Sample size 5 10 5 Sample mean 4 8 9 ​ The overall mean for all the treatments is ______.

7.25

In an analysis of variance where the total sample size for the experiment is nT and the number of populations is k, the mean square within treatments is _____.

SSE/(nT - k)

The proportion of the variation in the dependent variable y that is explained by the estimated regression equation is measured by the _____.

coefficient of determination

If the coefficient of correlation is .4, the percentage of variation in the dependent variable explained by the estimated regression equation _____.

is 16%

A procedure used for finding the equation of a straight line that provides the best approximation for the relationship between the independent and dependent variables is ______.

the least squares method

Exhibit 10-6 The management of a department store is interested in estimating the difference between the mean credit purchases of customers using the store's credit card versus those customers using a national major credit card. You are given the following information. Assume the samples were selected randomly. Store's Card Major Credit Card Sample size 64 49 Sample mean $140 $125 Population standard deviation $10 $8 Refer to Exhibit 10-6. A point estimate for the difference between the mean purchases of the users of the two credit cards (Store's Card - Major Credit Card) is _____.

15

The F ratio in a completely randomized ANOVA is the ratio of _____.

MSTR/MSE