A)Test the significance of the population correlation coefficient r (t-test using        α = 5%)

B)Test the significance of the population regression coefficient b₁ (t-test using        α = 5%)

C)Interpret the Coefficient of Determination as measure of the goodness of the fit (R²). Data sets are below and Thanks!

Problem 31. Calculate the expected value and variance of X for each of the following scenarios.

1. X = {0, 1} where each has equal probability. (A coin flip)

2. X = {1, 2, 3, 4, 5, 6} where each has equal probability. (A die roll)

3. X = {0, 1} with f(0) = 1/3 and f(1) = 2/3.

4. X = B(3, 0.35). (Use info from Problem 26.)(Problem 26. Let X = B(3, 0.35). Calculate each f(k) and the sum X 3 k=0 f(k).)

Problem 32. Calculate the expected value and variance of X = B(3, 0.35) by using Theorem 41. Compare the results to part 4 of Problem 31.

Problem 33. Let (X, f) be a CPD. Show that P(X = x) = 0 for any x ∈ X.

Problem 34. Consider f : R → R defined by f(x) = 1 1 + x 2 . Explain why f is not a PDF, and find a constant c so that cf is a PDF.

Problem 35. Let F be a CDF for a CPD (X, f). Find lim x→−∞ F(x) and limx→∞ F(x).

The American Heart Association is about to conduct an anti-smoking campaign and wants to know the fraction of Americans over 42 who smoke.

Step 2 of 2:

Suppose a sample of 897 Americans over 42 is drawn. Of these people, 637 don't smoke. Using the data, construct the 95%confidence interval for the population proportion of Americans over 42 who smoke. Round your answers to three decimal places.

You are the foreman of the Bar-S cattle ranch in Colorado. A neighboring ranch has calves for sale, and you are going to buy some calves to add to the Bar-S herd. How much should a healthy calf weigh? Let x be the age of the calf (in weeks), and let y be the weight of the calf (in kilograms). x 1 5 11 16 26 36 y 39 47 73 100 150 200 Complete parts (a) through (e), given Σx = 95, Σy = 609, Σx2 = 2375, Σy2 = 81,559, Σx y = 13,777, and r ≈ 0.997.

(a) Make a scatter diagram of the data. (Select the correct graph.) A scatter diagram with 6 points is graphed on the x y coordinate plane.

The points are located at (1, 39), (5, 47), (11, 73), (16, 100), (26, 150), (36, 200). When considering the data points as a whole, the points are loosely gathered into a mass that is lower on the left and higher on the right. A scatter diagram with 6 points is graphed on the x y coordinate plane.

The points are located at (1, 29), (5, 37), (11, 63), (16, 90), (26, 140), (36, 190). When considering the data points as a whole, the points are loosely gathered into a mass that is lower on the left and higher on the right. A scatter diagram with 6 points is graphed on the x y coordinate plane.

The points are located at (3, 29), (7, 37), (13, 63), (18, 90), (28, 140), (38, 190). When considering the data points as a whole, the points are loosely gathered into a mass that is lower on the left and higher on the right. A scatter diagram with 6 points is graphed on the x y coordinate plane.

The points are located at (3, 39), (7, 47), (13, 73), (18, 100), (28, 150), (38, 200). When considering the data points as a whole, the points are loosely gathered into a mass that is lower on the left and higher on the right. (b) Verify the given sums Σx, Σy, Σx2, Σy2, Σx y, and the value of the sample correlation coefficient r. (For each answer, enter a number. Round your value for r to three decimal places.) Σx = Σy = Σx2 = Σy2 = Σx y = r =

(c) Find x bar, and y bar. Then find the equation of the least-squares line y hat = a + b x. (For each answer, enter a number. Round your answers for x bar and y bar to two decimal places. Round your answers for a and b to three decimal places.) x bar = x bar = y bar = y bar = y hat = value of a coefficient + value of b coefficient x

(d) Graph the least-squares line. Be sure to plot the point (x bar, y bar) as a point on the line. (Select the correct graph.) A line and a point are graphed on the x y coordinate plane. The point is located the approximate point (15.8, 102). The line enters the window at approximately y = 171 on the positive y axis, goes down and right, passes through the approximate point (15.8, 102), and exits the window at approximately x = 39.1 on the positive x axis. A line and a point are graphed on the x y coordinate plane. The point is located the approximate point (15.8, 132). The line enters the window at approximately y = 201 on the positive y axis, goes down and right, passes through the approximate point (15.8, 132), and exits the window in the first quadrant. A line and a point are graphed on the x y coordinate plane. The point is located the approximate point (15.8, 132). The line enters the window at approximately y = 56 on the positive y axis, goes up and right, passes through the approximate point (15.8, 132), and exits the window in the first quadrant. A line and a point are graphed on the x y coordinate plane. The point is located the approximate point (15.8, 102). The line enters the window at approximately y = 26 on the positive y axis, goes up and right, passes through the approximate point (15.8, 102), and exits the window in the first quadrant.

(e) Find the value of the coefficient of determination r2. What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? What percentage is unexplained? (For each answer, enter a number. Round your answer for r2 to three decimal places. Round your answers for the percentages to one decimal place.) r2 = explained = % unexplained = %

(f) The calves you want to buy are 20 weeks old. What does the least-squares line predict for a healthy weight (in kg)? (Enter a number. Round your answer to two decimal places.) kg

Create an excel worksheet and populate it, in columns, with values of X that are -2, -1, 0, 1, 2 and values of Y that are -1, 1,1,1,3. As an aside, note that the sample mean of X is 0. Create the columns shown below, and enter the proper formulas into excel.

SupposeSuppose the heights of 18-year-old men are approximately normally distributed, with mean 66 inches and standard deviation 1 inches.

(a) What is the probability that an 18-year-old man selected at random is between 65 and 67 inches tall? (Round your answer to four decimal places.)


(b) If a random sample of nine 18-year-old men is selected, what is the probability that the mean height x is between 65 and 67 inches? (Round your answer to four decimal places.)


(c) Compare your answers to parts (a) and (b). Is the probability in part (b) much higher? Why would you expect this?

The probability in part (b) is much higher because the standard deviation is smaller for the x distribution.

The probability in part (b) is much higher because the standard deviation is larger for the x distribution.    

The probability in part (b) is much higher because the mean is smaller for the x distribution.

The probability in part (b) is much higher because the mean is larger for the x distribution.

The probability in part (b) is much lower because the standard deviation is smaller for the x distribution.

Use of statistic in the mathematics? Explain in a broad way.

What are some of the predictive technologies used in condition-based maintenance (CBM)? Please name five and describe them briefly.

The state of Virginia has implemented a Standard of Learning (SOL) test that all public school students must pass before they can graduate from high school. A passing grade is 75. Montgomery County High School administrators want to gauge how well their students might do on the SOL test, but they don’t want to take the time to test the whole student population. Instead, they selected 20 students at random and gave them the test. The results are as follows:
83    79    56    93
48    92    37    45
72    71    92    71
66    83    81    80
58    95    67    78

Assume that SOL test scores are normally distributed.

1. Compute the mean and standard deviation for these dat
2. Determine the probability that a student at the high school will pass the test.
3. How many percent of students will receive a score between 75 and 95?
4. What score will put a student in the bottom 15% in SOL score among all students who take the test?
5. What score will put a student in the top 2% in SOL score among all students who take the test?

PLEASE USE EXCEL

THANK YOU

Racism, juries, and interactions: In a study of racism, Nail, Harton and Decker (2003) had participants read a scenario in which a police officer assaulted a motorist. Half the participants read about an African American officer who assaulted an European American motorist, and half read about a European American officer who assaulted an African American motorist. Participants were categorized based on political orientation: liberal, moderate, or conservative. Participants were told that the officer was acquitted on assault charges in state court but found guilty of violating the motorist’s rights in federal court. Double jeopardy occurs when an individual is tried twice for the same crime. Participants were asked to rate, on a scale of 1-7, the degree to which the officer had been placed in double jeopardy by the second trial. The researchers reported the interaction as F= (2,58)=10.93, p<0.0001. The means for the liberal participants were 3.18 for those who read about the African American officer and 1.91 for those who read about the European American officer. The mean for the moderate participants were 3.50 for those who read about the African American officer and 3.33 for those who read about the European American officer. The means for the conservative participants were 1.25 for those who read about the African American officer and 4.62 for those who read about the European American officer.

a. Draw a table of cell means that includes that actual means for this study.

b. Do the reported statistics indicate that there is a significant interaction? If yes, describe the interaction in your own words.

c. Draw a bar graph that depicts the interaction. Include lines that connect the tops of the bars and show the pattern of the interaction.

d. Is this quantitative or qualitative interaction? Explain

e. Change the cell mean for the conservative participants who read about an African American officer so that this is now a quantitative interaction.

f. Draw a bar graph that depicts the patter that includes the new cell means

g. Change the cell means for the moderate and conservative participants who reads about an African American officer so that there is now no interaction.

h. Draw a bar graph that depicts the pattern that includes the new cell means.

16 Let ? have a normal distribution with ?(?) = 0.2 and ??(?) = 0.08. a. Find ?(? < 0.36) e. Find ? such that ?(? ≤ ?) = 0.05. b. Find ?(? > 0.16) f. Find ? such that ?(? ≥ ?) = 0.10. c. Find ?(? ≥ 0.60) g. Find ? such that ?(? > ?) = 0.80. d. Find 0.28 < ? ≤ 0.40) h. Find ? such that ?(? < ?) = 0.95.

Wally runs a fruit & vege stall Wally’s VegeRama -at the local Sunday market. He can buy watermelons from his supplier for $5 each. He can sell watermelons for $10 Each. On any particular Sunday, demand for watermelons follows a Poisson distribution with mean 5. Any watermelons that are not sold on Sunday go bad before the next weekend. Wally’s current policy is to stock 6 watermelons.

2. How many watermelons should Wally stock to maximise his expected profit? expected profit is 3.0800

Can someone just answer 8 A B C D and E please!!!

Regression Analysis (Excel 2010 & 2007)

1.         Open a new Excel worksheet (which will be saved as REGRESSION.xlsx).  In cell A1 type your name.  In cell A2 type the course and section number (i.e. ECON225-01).  In cell A3 type the date.  Skip cell A4.  In cell A5 type “Assignment: Regression Analysis”.  In cell A6 type “File: REGRESSION.xlsx”.

2.         Type X in cell B8 and type Yin cell C8.  Type Miles in cell B9 and type Minutes  in cell C9.

In cells B10 through B18 enter the following values:

11, 10, 15, 7, 3, 6, 9, 12, 5

                        In cells C10 through C18, enter the following data values:  

                        28, 27, 35, 15, 8, 14, 20, 29, 13  

            Center format cells B8 through C18 for a more professional appearance.

3.         Click on the Datatab in the toolbar, then select Data Analysis. Next, select   Regressionfrom the Analysis Tools and click on OK.  In the Regression dialog boxes type C10:C18in the Input Y Range dialog box, then type B10:B18in the Input X Range dialog box.  Under Output Options select Output Range and type A20:I40in the output range dialog box.  Click onOK. A Summary Output table will appear.

4.         Select cell D27 and type Forecast for Y when X = 13:  Next select cell G27, then click on the Formulas tabin the toolbar, then select More Functions. Under the Function category select Statistical.  Under the Function name select  FORECAST.  In the dialog boxes type 13in the X dialog box, type C10:C18in the Known Y’s dialog box, and type B10:B18in the Known X’s dialog box.  Click on OK. The forecasted value for Y when X=13 will appear in cell G27.

5.         Return to the Home tab in the toolbar.  Select the columns of X and Y data values from B10 through C18(do not select their headings).  Next, click on the Insert tabin the toolbar, under Charts select Scatter, then select the first choice of a scatter diagram graph.    Resize and reposition the scatter diagram to the location of cell E9 for the top left corner of the diagram, and cell I 22 for the bottom right corner of the diagram.  (This will allow everything to fit on one printed page.) Delete the “Series 1” label box. You can label the axes with the variable names (Miles and Minutes) by clicking on the outside corner of the graph, then select Axis Titles in the toolbar. Label both the X and Y axes of the graph with their appropriate variable names.

            (Instructions continue on the next page.)

6.         Next, click any place inside of the scatter diagram. Under the Analysis options, click on Trendline,thenselectLinear Trendline. Click on OK. A trend line will be added to the scatter diagram.  Do a Print Preview to make sure that your graph fits onto the printed page.

7.         Save your worksheet on a disk as REGRESSION.xlsx and print-out the worksheet to submit to the instructor.  

8.         In addition to submitting a print-out of the worksheet(s), also submit typed answers to the following questions, referencing the data in your print-out and your textbook or Notes:

(a)        What is the regression equation for this data set? (Write the printed “a” and “b” values into the equation.  Hint: Under the Coefficient column the value for the Intercept is the value for “a” and the X Variable value is the value for “b”.)

(b)       Interpret the printed value for “a” relative to its definition, the X and Y variable names, and its value.  

(c)        Interpret the printed value for “b” relative to its definition, the X and Y variable names, and its value.

(d)       Interpret the printed value for “r” relative to its definition, the X and Y variable names, and its value.  (**Hint: Under the Regression Statistics section the Multiple R value is the correlation coefficient and the R Square value is the Coefficient of Determination.  The printed table value for “r” does not always indicate direction (+ or -), therefore, check that the sign for your “r” value agrees with the sign for your “b” value.)  

(e)        Interpret the printed value for “r²” relative to its definition, the X and Y variable names, and its value.