Question 1

Cause of High Blood PressureSome studies have shown that there is a correlation betweenconsumption of salt and blood pressure. As more salt is consumed, blood pressure tends to rise. Areporter reads one of those studies and writes the headline "Increased Salt Consumption CausesBlood Pressure to Rise." Is that headline justified? If not, help this reporter by rewriting theheadline so that it is correct.

Question 2

Weight Loss and Correlation (part 1)In a test of the Weight Watchers weight loss program,the weights of 40 subjects are recorded before and after the program. Assume that the before/afterweights result inr= 0.876. Is there sufficient evidence to support a claim of a linear correlationbetween the before/after weights? Does the value ofrindicate that the program is effective inreducingweight? Why or why not?

Use the Correlation Table, Table A-6, inthe file"Formulas andTables" andassume a0.05significancelevelto answer this question.

Choose the correct critical value from the possibilities below.

Group of answer choices

0.402

0.312

0.294

0.335

Question 3

Weight Loss and Correlation (part 2)In a test of the Weight Watchers weight loss program,the weights of 40 subjects are recorded before and after the program. Assume that the before/afterweights result inr= 0.876. Is there sufficient evidence to support a claim of a linear correlationbetween the before/after weights? Does the value ofrindicate that the program is effective inreducingweight? Why or why not?

Compare the correlation coefficient to the critical value. Which of the following statements is the most accurate?

Group of answer choices

The correlation coefficient is greater than the critical value. We would fail to reject the null hypothesis that there is no correlation. This sample suggests that no relationship exists between the before and after weights.

The correlation coefficient is less than the critical value. We would reject the null hypothesis that there is no correlation. This sample suggests that a relationship exists between the before and after weights.

The correlation coefficient is greater than the critical value. We would reject the null hypothesis that there is no correlation. This sample suggests that a relationship exists between the before and after weights.

The correlation coefficient is greater than the critical value. We would reject the null hypothesis that there is no correlation. This sample suggests that no relationship exists between the before and after weights.

Question 4

Importance of Graphing.Belowis a data set from "graphs in Statistical Analysis," by F.J.Anscombe,The American Statistician, Vol. 27. For this data set:

X	7	5	10	8	13	9	11	14	6	4	12
Y	6.42	5.73	7.46	6.77	12.74	7.11	7.81	8.84	6.08	5.39	8.15

Construct a scatterplot following the directions below using a

TI-83/84 Plus. welcome to use other forms of technology as well

1. Press STAT & choose 1: Edit

2. Enter the data fromxinto L1 (press ENTER between each value)

3.Enter the data fromyinto L2(press ENTER between each value)

4. Press 2NDand then Y=(STAT PLOT)andhighlight1: Plot 1...Off

5. Press ENTER toturn ON Plot 1. Make sure that Xlist is L1 and Ylist is L2.

6. Select the first type of plot and make sure all other graphs are turned off.

7.Toviewthe data points in the best window possible, press ZOOM&

thenhighlight9: ZoomStat&press ENTER

8. take a photo of the resulting scatter plot window.

Question 5

Finding the linear correlation.Belowis a data set from "graphs in Statistical Analysis," by F.J.Anscombe,The American Statistician, Vol. 27. For this data set:

X	7	5	10	8	13	9	11	14	6	4	12
Y	6.42	5.73	7.46	6.77	12.74	7.11	7.81	8.84	6.08	5.39	8.15

Find the value of the linear correlation coefficientr. The instructions below walk you through how to find itusing aTI-83/84 Plus. You are welcome to use other forms of technology as well.

1. Press STAT & choose tests & selectLinRegTTest& Press ENTER

2.Make sure that Xlist is L1.

3. Make sure thatYlist is L2.

4.Make sure Freq is 1.

5.For the&,highlight the0 choice

6.Next to the RegEq we want to enter Y1,to do so, place the cursor next to

the RegEq and then press[VARS], move the cursor to highlight the Y-Vars

menu, the first choice should bev1: Function, press 1 or [ENTER],

the newmenushould yield a list of y-vars, the first choice should be 1:Y1,

just press[ENTER]and you should return to the line RegEq and the Y1

should bewhere you want it(you should not have to complete step again unless youerase the calculatormemory).

7.Select"Calculate"and press ENTER.

8. Recordr

Enter the value for r rounding to three decimal places.

Question 6

Testing the LinearCorrelation.Use the data from the previous question and the correlation coefficient you calculated to answer the following question.

Use the correlation table, Table A-6 (in the file formulas & tables)forn= 11 with asignificancelevel of = 0.05,to find thecritical value necessary to test if the correlation between the two variables is significant.

Enter the critical value exactly as it appears in the table.

Question 7

Testing the LinearCorrelation.Use the results from questions #5 and #6 to determine whether there is sufficient evidence to support the claim of linear correlation between the twovariables. Fill the in the blanks of the following statement.

"As the correlation coefficient is [ Select ] ["greater than", "less than"] than the critical value, the evidence [ Select ] ["does", "does not"] support the claim of a linear correlation between the two variables.

Question 8

Identify the feature of the data that would be missed if the previous problem was completedwithout constructing thescatterplot in question #4.

Choose the best response below based on the data set in question #4.

Group of answer choices

The fact that the y values increase as the x values increase.

The linear relationship between the data points.

There is an outlier in the data.

The middle value of the data.

Question 9

Blood PressureMeasurementsListed below are systolic blood pressure measurements(mmHg)obtainedfrom the same woman (based on data from "Consistency of Blood PressureDifferences Between the Left and Right Arms," by Eguchi, et al.,Archives of Internal Medicine,Vol.167).

Right	102	101	94	79	79
Left	175	169	182	146	144

Find the value of the linear correlation coefficientr. The instructions below walk you through how to find itusing aTI-83/84 Plus. You are welcome to use other forms of technology as well.

1. Press STAT & choose tests & selectLinRegTTest& Press ENTER

2.Make sure that Xlist is L1.

3. Make sure thatYlist is L2.

4.Make sure Freq is 1.

5.For the&,highlight the0 choice

6.Next to the RegEq we want to enter Y1,to do so, place the cursor next to

the RegEq and then press[VARS], move the cursor to highlight the Y-Vars

menu, the first choice should bev1: Function, press 1 or [ENTER],

the newmenushould yield a list of y-vars, the first choice should be 1:Y1,

just press[ENTER]and you should return to the line RegEq and the Y1

should bewhere you want it(you should not have to complete step again unless youerase the calculatormemory).

7.Select"Calculate"and press ENTER.

8. Recordr

Enter the value for r rounding to three decimal places.

Question 10

Blood PressureMeasurementsListed below are systolic blood pressure measurements(mmHg)obtainedfrom the same woman (based on data from "Consistency of Blood PressureDifferences Between the Left and Right Arms," by Eguchi, et al.,Archives of Internal Medicine,Vol.167).

Right	102	101	94	79	79
Left	175	169	182	146	144

Find the value of the linear correlation coefficientr. The instructions below walk you through how to find itusing aTI-83/84 Plus. You are welcome to use other forms of technology as well.

1. Press STAT & choose tests & selectLinRegTTest& Press ENTER

2.Make sure that Xlist is L1.

3. Make sure thatYlist is L2.

4.Make sure Freq is 1.

5.For the&,highlight the0 choice

6.Next to the RegEq we want to enter Y1,to do so, place the cursor next to

the RegEq and then press[VARS], move the cursor to highlight the Y-Vars

menu, the first choice should bev1: Function, press 1 or [ENTER],

the newmenushould yield a list of y-vars, the first choice should be 1:Y1,

just press[ENTER]and you should return to the line RegEq and the Y1

should bewhere you want it(you should not have to complete step again unless youerase the calculatormemory).

7.Select"Calculate"and press ENTER.

8. Notice the in the output a p-value is listed. We can use the P-value instead of the critical value and correlation coefficient to make a determination.

Enter the p-value from the output here. Round to two decimal places.

Question 11

Blood PressureMeasurementsListed below are systolic blood pressure measurements(mmHg)obtainedfrom the same woman (based on data from "Consistency of Blood PressureDifferences Between the Left and Right Arms," by Eguchi, et al.,Archives of Internal Medicine,Vol.167).

Based on the result in question #9 and the p-value from question #10, what conclusion would you draw regarding the correlation between the two arms?

Conduct the test at a 1% significance level.

Fill the blanks below to draw the conclusion.

"Since the p-value here is [ Select ] ["Greater than", "Less Than"] the alpha value of 0.01, we would [ Select ] ["reject", "fail to reject"] the null hypothesis that there is no correlation. The sample evidence, in this case, would lead us to conclude that there [ Select ] ["is", "is not"] a linear relationship between the blood pressure readings on the right and left arm.