A mathematics department has been experimenting with four different delivery methods for content in their Algebra courses. One method is the traditional lecture (method I), the second is a hybrid format with half the class time online and the other half face-to-face (method II), the third is online (method III), and the fourth is a model from which students obtain their lectures and do their work in a lab with an instructor available for assistance (method IV). To assess the effectiveness of the four methods, students in each approach are given a final exam with the results shown in the accompanying table. Do the data suggest that any method has a different mean score from the others?

The data table:

Method_I Method_II Method_III Method_IV 78 88 78 87 77 56 61 93 82 82 67 77 68 71 69 58 86 61 65 83 72 40 74 69 80 62 66 60 61 90 .

The table of critical values for the correlation coefficient: Sample Size_n Critical_Value 5 0.880 6 0.888 7 0.898 8 0.906 9 0.912 10 0.918 11 0.923 12 0.928 13 0.932 14 0.935 15 0.939 16 0.941 17 0.944 18 0.946 19 0.949 20 0.951 21 0.952 22 0.964 23 0.956 24 0.957 25 0.959 30 0.960 .

(a) What is the response variable in this study? Is it qualitative or quantitative? The response variable is delivery mechanism. final exam score. This variable is quantitative. qualitative.

Part 2 (b) What is the factor in this study? How many levels does it have? The factor is final exam score. delivery mechanism. It has enter your response here levels.

Part 3 (c) Write the null and alternative hypotheses. Choose the correct answer below. A. Upper H 0 : at least one of the means is different and Upper H 1 : mu Subscript Upper I Baseline equals mu Subscript II Baseline equals mu Subscript III Baseline equals mu Subscript IV B. Upper H 0 : mu Subscript Upper I Baseline equals mu Subscript II Baseline equals mu Subscript III Baseline equals mu Subscript IV and Upper H 1 : at least one of the means is different C. Upper H 0 : mu Subscript Upper I Baseline equals mu Subscript II Baseline equals mu Subscript III Baseline equals mu Subscript IV and Upper H 1 : mu Subscript Upper I Baseline less than mu Subscript II Baseline less than mu Subscript III Baseline less than mu Subscript IV D. Upper H 0 : mu Subscript Upper I Baseline equals mu Subscript II and Upper H 1 : the means are different

Part 4 (d) State the requirements that must be satisfied to use the one-way ANOVA procedure. Select all that apply. A. The k samples must be independent of each other. B. There must be k simple random samples, one from each of k populations. C. The populations must be normally distributed and have the same mean. D. There must be k simple random samples, each from the same population. E. The populations must be normally distributed and have the same variance.

Part 5 (e) Assuming the requirements stated in part (d) are satisfied, use the following one-way ANOVA table to test the hypothesis of equal means at the alphaequals0.05 level of significance. ANOVA Table Source DF SS MS F P Factor 3 810.13 270.04 2.08 0.127 Error 26 3370.83 129.65 Total 29 4180.97 Part 6 Should the null hypothesis be rejected? Do not reject Reject Upper H 0; there is sufficient insufficient evidence to conclude that a method has a different mean score from the others.

Part 7 (f) Shown are side-by-side boxplots of each method. Do these boxplots support the results obtained in part (e)? A. Yes, because the boxplots do not show that at least one of the means is significantly different. B. Yes, because the boxplots show that at least one of the means is significantly different. C. No, because the boxplots show that all of the means are significantly different. D. No, because the boxplots show that the means are not significantly different. Final Exam Score by Method of Delivery 40 60 80 100 Method III Method II Method I Method IV Score Delivery Method

Four horizontal boxplots collectively titled "Final Exam Score by Method of Delivery" have a horizontal x-axis labeled "Score" from less than 40 to 100 in increments of 20 and a vertical axis labeled "Delivery Method" with labels "Method Roman Numeral One," "Method Roman Numeral Two," "Method Roman Numeral Three," and "Method Roman Numeral Four." The boxplot corresponding with "Method Roman Numeral Four" consists of a box extending from 70 to 88 with a vertical line running through the box at 80 and two horizontal line segments extending from the left and right sides of the box to 58 and 94, respectively. The boxplot corresponding with "Method Roman Numeral Three" consists of a box extending from 66 to 74 with a vertical line running through the box at 68 and two horizontal line segments extending from the left and right sides of the box to 62 and 78, respectively. The boxplot corresponding with "Method Roman Numeral Two" consists of a box extending from 58 to 76 with a vertical line running through the box at 62 and two horizontal line segments extending from the left and right sides of the box to 40 and 88, respectively. The boxplot corresponding with "Method Roman Numeral One" consists of a box extending from 68 to 82 with a vertical line running through the box at 78 and two horizontal line segments extending from the left and right sides of the box to 62 and 90, respectively. All values are approximate. Part 8 (g) Interpret the P-value. Select the correct choice below and fill in the answer box within your choice. (Round to three decimal places as needed.) A. Assuming the null hypothesis is true, the probability this much or more variability occurs in the four sample means is enter your response here when the experiment is repeated many times. B. Assuming the null hypothesis is false, the probability this much or more variability occurs in the four sample means is enter your response here when the experiment is repeated many times. C. Assuming the null hypothesis is false, the probability this much or more variability occurs in the four sample means is enter your response here in every experiment. D. Assuming the null hypothesis is true, the probability this much or more variability occurs in the four sample means is enter your response here in every experiment.

Part 9 (h) Verify that the residuals are normally distributed. The normal probability plot and linear correlation coefficient, r, is shown below. How does the normal probability plot of the residuals show that the residuals are normally distributed? A. The plot is linear enough because r is greater than the critical value. B. The plot is not linear enough because r is greater than the critical value. C. The plot is linear enough because r is less than the critical value. D. The plot is not linear enough because r is less than the critical value. E. There is at least one outlier. (a) What is the response variable in this study? Is it qualitative or quantitative?

The response variable is

delivery mechanism.

final exam score.

This variable is

quantitative.

qualitative.

Part 2

(b) What is the factor in this study? How many levels does it have?

The factor is

final exam score.

delivery mechanism.

It has

enter your response here

levels.

Part 3

(c) Write the null and alternative hypotheses. Choose the correct answer below.

A.

Upper H 0 : at least one of the means is differentH0:atleastoneofthemeansisdifferent

and Upper H 1 : mu Subscript Upper I Baseline equals mu Subscript II Baseline equals mu Subscript III Baseline equals mu Subscript IVH1:I=II=III=IV

B.

Upper H 0 : mu Subscript Upper I Baseline equals mu Subscript II Baseline equals mu Subscript III Baseline equals mu Subscript IVH0:I=II=III=IV

and Upper H 1 : at least one of the means is differentH1:atleastoneofthemeansisdifferent

C.

Upper H 0 : mu Subscript Upper I Baseline equals mu Subscript II Baseline equals mu Subscript III Baseline equals mu Subscript IVH0:I=II=III=IV

and Upper H 1 : mu Subscript Upper I Baseline less than mu Subscript II Baseline less than mu Subscript III Baseline less than mu Subscript IVH1:I

D.

Upper H 0 : mu Subscript Upper I Baseline equals mu Subscript IIH0:I=II

and Upper H 1 : the means are differentH1:themeansaredifferent

Part 4

(d) State the requirements that must be satisfied to use the one-way ANOVA procedure. Select all that apply.

A.

The k samples must be independent of each other.

B.

There must be k simple random samples, one from each of k populations.

C.

The populations must be normally distributed and have the same mean.

D.

There must be k simple random samples, each from the same population.

E.

The populations must be normally distributed and have the same variance.

Part 5

(e) Assuming the requirements stated in part (d) are satisfied, use the following one-way ANOVA table to test the hypothesis of equal means at the

alphaequals=0.05

level of significance.

ANOVA Table
Source	DF	SS	MS	F	P
Factor	33	810.13810.13	270.04270.04	2.082.08	0.1270.127
Error	2626	3370.833370.83	129.65129.65
Total	2929	4180.974180.97

Part 6

Should the null hypothesis be rejected?

Do not reject

Reject

Upper H 0H0;

there is

sufficient

insufficient

evidence to conclude that a method has a different mean score from the others.

Part 7

(f) Shown are side-by-side boxplots of each method. Do these boxplots support the results obtained in part (e)? A. Yes, because the boxplots do not show that at least one of the means is significantly different. B. Yes, because the boxplots show that at least one of the means is significantly different. C. No, because the boxplots show that all of the means are significantly different. D. No, because the boxplots show that the means are not significantly different.

Final Exam Score by Method of Delivery 406080100MethodIIIMethodIIMethodIMethodIVScoreDeliveryMethod Four horizontal boxplots collectively titled "Final Exam Score by Method of Delivery" have a horizontal x-axis labeled "Score" from less than 40 to 100 in increments of 20 and a vertical axis labeled "Delivery Method" with labels "Method Roman Numeral One," "Method Roman Numeral Two," "Method Roman Numeral Three," and "Method Roman Numeral Four." The boxplot corresponding with "Method Roman Numeral Four" consists of a box extending from 70 to 88 with a vertical line running through the box at 80 and two horizontal line segments extending from the left and right sides of the box to 58 and 94, respectively. The boxplot corresponding with "Method Roman Numeral Three" consists of a box extending from 66 to 74 with a vertical line running through the box at 68 and two horizontal line segments extending from the left and right sides of the box to 62 and 78, respectively. The boxplot corresponding with "Method Roman Numeral Two" consists of a box extending from 58 to 76 with a vertical line running through the box at 62 and two horizontal line segments extending from the left and right sides of the box to 40 and 88, respectively. The boxplot corresponding with "Method Roman Numeral One" consists of a box extending from 68 to 82 with a vertical line running through the box at 78 and two horizontal line segments extending from the left and right sides of the box to 62 and 90, respectively. All values are approximate.

Part 8

(g) Interpret the P-value. Select the correct choice below and fill in the answer box within your choice.

(Round to three decimal places as needed.)

A.

Assuming the null hypothesis is true, the probability this much or more variability occurs in the four sample means is

enter your response here

when the experiment is repeated many times.

B.

Assuming the null hypothesis is false, the probability this much or more variability occurs in the four sample means is

enter your response here

when the experiment is repeated many times.

C.

Assuming the null hypothesis is false, the probability this much or more variability occurs in the four sample means is

enter your response here

in every experiment.

D.

Assuming the null hypothesis is true, the probability this much or more variability occurs in the four sample means is

enter your response here

in every experiment.

Part 9

(h) Verify that the residuals are normally distributed. The normal probability plot and linear correlation coefficient, r, is shown below. How does the normal probability plot of the residuals show that the residuals are normally distributed?

A. The plot is linear enough because r is greater than the critical value. B. The plot is not linear enough because r is greater than the critical value. C. The plot is linear enough because r is less than the critical value. D. The plot is not linear enough because r is less than the critical value. E. There is at least one outlier.

Probability Plot of Residuals -25.523.5-33Residualsz-score A normal probability plot titled "Probability Plot of Residuals" has a horizontal axis labeled "Residuals" from less than negative 14.4 to 14.4 plus in increments of 4.8 and vertical axis labeled "z-score" from less than negative 2 to 2 plus in increments of 1. There are dashed lines along the axes. 30 plotted points tightly follow the pattern of a plotted line that rises from left to right, passing through the points (negative 11, negative 1) and (11, 1). The leftmost point is at (negative 25, negative 2) and the rightmost point is at (23, 2). All values are approximate.

requals=0.9940.994

(a) What is the response variable in this study? Is it qualitative or quantitative? The response variable is delivery mechanism. final exam score. This variable is quantitative. qualitative. Part 2 (b) What is the factor in this study? How many levels does it have? The factor is final exam score. delivery mechanism. It has enter your response here levels. Part 3 (c) Write the null and alternative hypotheses. Choose the correct answer below. A. Upper H 0 : at least one of the means is different and Upper H 1 : mu Subscript Upper I Baseline equals mu Subscript II Baseline equals mu Subscript III Baseline equals mu Subscript IV B. Upper H 0 : mu Subscript Upper I Baseline equals mu Subscript II Baseline equals mu Subscript III Baseline equals mu Subscript IV and Upper H 1 : at least one of the means is different C. Upper H 0 : mu Subscript Upper I Baseline equals mu Subscript II Baseline equals mu Subscript III Baseline equals mu Subscript IV and Upper H 1 : mu Subscript Upper I Baseline less than mu Subscript II Baseline less than mu Subscript III Baseline less than mu Subscript IV D. Upper H 0 : mu Subscript Upper I Baseline equals mu Subscript II and Upper H 1 : the means are different Part 4 (d) State the requirements that must be satisfied to use the one-way ANOVA procedure. Select all that apply. A. The k samples must be independent of each other. B. There must be k simple random samples, one from each of k populations. C. The populations must be normally distributed and have the same mean. D. There must be k simple random samples, each from the same population. E. The populations must be normally distributed and have the same variance. Part 5 (e) Assuming the requirements stated in part (d) are satisfied, use the following one-way ANOVA table to test the hypothesis of equal means at the alphaequals0.05 level of significance. ANOVA Table Source DF SS MS F P Factor 3 810.13 270.04 2.08 0.127 Error 26 3370.83 129.65 Total 29 4180.97 Part 6 Should the null hypothesis be rejected? Do not reject Reject Upper H 0; there is sufficient insufficient evidence to conclude that a method has a different mean score from the others. Part 7 (f) Shown are side-by-side boxplots of each method. Do these boxplots support the results obtained in part (e)? A. Yes, because the boxplots do not show that at least one of the means is significantly different. B. Yes, because the boxplots show that at least one of the means is significantly different. C. No, because the boxplots show that all of the means are significantly different. D. No, because the boxplots show that the means are not significantly different. Final Exam Score by Method of Delivery 40 60 80 100 Method III Method II Method I Method IV Score Delivery Method

Four horizontal boxplots collectively titled "Final Exam Score by Method of Delivery" have a horizontal x-axis labeled "Score" from less than 40 to 100 in increments of 20 and a vertical axis labeled "Delivery Method" with labels "Method Roman Numeral One," "Method Roman Numeral Two," "Method Roman Numeral Three," and "Method Roman Numeral Four." The boxplot corresponding with "Method Roman Numeral Four" consists of a box extending from 70 to 88 with a vertical line running through the box at 80 and two horizontal line segments extending from the left and right sides of the box to 58 and 94, respectively. The boxplot corresponding with "Method Roman Numeral Three" consists of a box extending from 66 to 74 with a vertical line running through the box at 68 and two horizontal line segments extending from the left and right sides of the box to 62 and 78, respectively. The boxplot corresponding with "Method Roman Numeral Two" consists of a box extending from 58 to 76 with a vertical line running through the box at 62 and two horizontal line segments extending from the left and right sides of the box to 40 and 88, respectively. The boxplot corresponding with "Method Roman Numeral One" consists of a box extending from 68 to 82 with a vertical line running through the box at 78 and two horizontal line segments extending from the left and right sides of the box to 62 and 90, respectively. All values are approximate. Part 8 (g) Interpret the P-value. Select the correct choice below and fill in the answer box within your choice. (Round to three decimal places as needed.) A. Assuming the null hypothesis is true, the probability this much or more variability occurs in the four sample means is enter your response here when the experiment is repeated many times. B. Assuming the null hypothesis is false, the probability this much or more variability occurs in the four sample means is enter your response here when the experiment is repeated many times. C. Assuming the null hypothesis is false, the probability this much or more variability occurs in the four sample means is enter your response here in every experiment. D. Assuming the null hypothesis is true, the probability this much or more variability occurs in the four sample means is enter your response here in every experiment. Part 9 (h) Verify that the residuals are normally distributed. The normal probability plot and linear correlation coefficient, r, is shown below. How does the normal probability plot of the residuals show that the residuals are normally distributed? A. The plot is linear enough because r is greater than the critical value. B. The plot is not linear enough because r is greater than the critical value. C. The plot is linear enough because r is less than the critical value. D. The plot is not linear enough because r is less than the critical value. E. There is at least one outlier. Probability Plot of Residuals -25.5 23.5 -3 3 Residuals z-score

A normal probability plot titled "Probability Plot of Residuals" has a horizontal axis labeled "Residuals" from less than negative 14.4 to 14.4 plus in increments of 4.8 and vertical axis labeled "z-score" from less than negative 2 to 2 plus in increments of 1. There are dashed lines along the axes. 30 plotted points tightly follow the pattern of a plotted line that rises from left to right, passing through the points (negative 11, negative 1) and (11, 1). The leftmost point is at (negative 25, negative 2) and the rightmost point is at (23, 2). All values are approximate. requals0.994 The response variable isThis variable isThis variable isThe factor isIt hasIt haslevels.Choose the correct answer below.Select all that apply.Should the null hypothesis be rejected?Upper H 0Upper H 0; there isevidence to conclude that a method has a different mean score from the others.evidence to conclude that a method has a different mean score from the others.input field 2input field 3input field 4input field 5)Multiple Choice 5, Use arrow keys to hear answer options. Press space bar to select your answer.