The table below gives the age and bone density for five randomly selected women. Using this data, consider the equation of the regression line, yˆ=b0+b1xy^=b0+b1x, for predicting a woman's bone density based on her age. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant.

Table

Copy Data

Step 1 of 6 :  

Find the estimated slope. Round your answer to three decimal places.

Harley's Daycare will run a promotional raffle that offers a chance to win either a lifetime discount on merchandises (which results in a $1,000 savings) or a 5-year limited discount on any party-goods (which results in a $100 savings).

• Winning a lifetime discount has a 1-in-500 chance.

• Winning a 5-year limited discount has a 1-in-50 chance.

ONLY if you cannot answer F1, for partial credit (6 points) answer F2.

[F1 (13 points)] Some additional collected data is presented in the table below:

F2. Partial Credit. Answer to it ONLY if you cannot answer F1

Another survey examines the parent’s preference in having lunch provided by the SummerIsFun Co. or lunch brought from home, based on their children’s age. Some parents might not care, any possibility is OK.

a) Compute the Marginal Probabilities and the Joint Probabilities.

b) Compute: P(IT|H), P(IT or D)   

[G(28 points)]

Overall, the amount of days attended (per summer) is normally distributed around 35 days with a standard deviation of 4 days.

Do the seven steps for each word problem

Step 1: Establish null and alternate hypotheses

State the null and alternative hypothesis (as a sentence and formula).

Step 2: Calculate the degrees of freedom

Step 3: Calculate t _critical using critical t – table

Step 4: Calculate the Sum of Square deviation (SS_D)

Step 5: Calculate t _obtained

Step 6: Specify the critical value and the obtained value on a t-distribution curve

Step 7: Decision and Conclusion

Write a clear and concise conclusion.

A Pullman local sports store is interested in consumer purchasing likelihood of WSU gear (1=not at all to 7=very much) before and after a win in football. A researcher picks 10 WSU students as the participants of the study. The data are shown below. Use alpha = .01 to see whether a win in football increases consumers’ likelihood of buying WSU gear.

After: 4 5 5 6 5 7 5 6 3 4

Before: 3 5 4 4 5 6 5 4 3 3

A marketing researcher has heard that when kids are anonymous, they'll take more candy. To test this hypothesis, she brings 6 kids into a specially-constructed Halloween Lab with two rooms. Each room is identically decorated and contains a decorated front porch, a front door, and a doorbell. Behind the door is a confederate who will answer the door and offer a bowl of candy. The two rooms differ only in their lighting conditions. One room is light; one room is dark, the latter presumably leading to greater anonymity. She says, ok kids, I want you to go into each room and interact with the person behind the door as you would normally interact during Halloween. Ring the doorbell, say trick or treat, and then take some candy. So, the kids do this and the researcher measures how many pieces of candy they take. The data are shown below. Do kids take more candy under conditions that make them feel anonymous? Use alpha = .10.

Light Room:                  1          2          1          1          2          2

Dark Room:                  2          2          3          4          4          3

A toy company is concerned that its distribution strategy is not working. Sean Masterson, the marketing manager stated that one of the primary goals in the distribution of a particular toy is to keep the prices similar throughout all their distribution channels. To find out if their strategy is failing, the marketing department took a survey of 5 different outlets in three different channels. The price results are in the following table:

Using ANOVA, determine if there is a significant difference in prices between the three channels. Mr. Masterson wants to be 90% confident, so list all the steps of the hypothesis test and do the calculations then write a memorandum to Mr. Masterson stating your conclusion and backing it up with statistical analysis.

The Harleys Daycare. decided to use 20 different water balloon categories. Their prices (on 100 units) are listed below:

27           25           10           7              13           20           27           15           25           10          

22           16           11           9              12           20           17           17           23           20

a. Construct a grouped frequency distribution with 6 classes.           

Step 1. Find Range

Step 2. Given the number of classes, the width of each class is

Step 3. Create class boundaries

Step 4. Find the numerical frequencies

b. Use Excel to construct a Histogram. (Tools à Data Analysis à Histogram à for the input range, select the given values, for the bin range select the classes upper boundaries values à check Chart Output)

Note: If you don’t have the capability of using excel for the histogram, draw one by hand.

[D(14 points)] Consider the following set of data containing the amount of paid tuition/week for part-timers:

Z = ( X – U)/ σ where u is the mean and σ is the standard deviation.

a. For the set of data given above, calculate the following descriptive statistics (Briefly explain, especially the quartiles calculations. Use the rules given in the homework 2). For the rest you can use excel tools as long as you show your work.

b.   Compute the z-scores and enter them in the first given table. Give the formula you used.

c.   What type of skewness does this data set have? The data set has a left tail skewness.

Let (Un, U, n>1) be asequence of random variables such that Un and U are independent, Un is N(0, 1+1/n), and U is N(0,1), for each n≥1.

Calculate p(n)=P(|Un-U|<e), for all e>0.

Please give details as much as possible

Convert the following binomial distribution problems to normal distribution problems. Use the correction for continuity.

a. P(x ≤ 16| n = 30 and p = .70)

b. P(10 < x ≤ 20)| n = 25 and p = .50)

c. P(x = 22| n = 40 and p = .60)

d. P(x > 14| n = 16 and p = .45)

Of 12 possible building sites for factories, 5 have buried toxic waste sites that no one told

you about! If you choose 3 of the sites for initial building locations, what is the probability you

will be lucky enough to avoid any toxic waste sites?

Provide plots of the χ²(r) distributions (pdf) for values of r = 1,2,5,10,20.

A study of reading comprehension in children compared three methods of instruction. The three methods of instruction are called Basal, DRTA, and Strategies. Basal is the traditional method of teaching, while DRTA and Strategies are two innovative methods based on similar theoretical considerations. The READING data set includes three response variables that the new methods were designed to improve. Analyze these variables using ANOVA methods. Be sure to include multiple comparisons or contrasts as needed. Write a report summarizing your findings.

Reading:

subject group   pre1    pre2    post1   post2   post3
1       B       4       3       5       4       41
2       B       6       5       9       5       41
3       B       9       4       5       3       43
4       B       12      6       8       5       46
5       B       16      5       10      9       46
6       B       15      13      9       8       45
7       B       14      8       12      5       45
8       B       12      7       5       5       32
9       B       12      3       8       7       33
10      B       8       8       7       7       39
11      B       13      7       12      4       42
12      B       9       2       4       4       45
13      B       12      5       4       6       39
14      B       12      2       8       8       44
15      B       12      2       6       4       36
16      B       10      10      9       10      49
17      B       8       5       3       3       40
18      B       12      5       5       5       35
19      B       11      3       4       5       36
20      B       8       4       2       3       40
21      B       7       3       5       4       54
22      B       9       6       7       8       32
23      D       7       2       7       6       31
24      D       7       6       5       6       40
25      D       12      4       13      3       48
26      D       10      1       5       7       30
27      D       16      8       14      7       42
28      D       15      7       14      6       48
29      D       9       6       10      9       49
30      D       8       7       13      5       53
31      D       13      7       12      7       48
32      D       12      8       11      6       43
33      D       7       6       8       5       55
34      D       6       2       7       0       55
35      D       8       4       10      6       57
36      D       9       6       8       6       53
37      D       9       4       8       7       37
38      D       8       4       10      11      50
39      D       9       5       12      6       54
40      D       13      6       10      6       41
41      D       10      2       11      6       49
42      D       8       6       7       8       47
43      D       8       5       8       8       49
44      D       10      6       12      6       49
45      S       11      7       11      12      53
46      S       7       6       4       8       47
47      S       4       6       4       10      41
48      S       7       2       4       4       49
49      S       7       6       3       9       43
50      S       6       5       8       5       45
51      S       11      5       12      8       50
52      S       14      6       14      12      48
53      S       13      6       12      11      49
54      S       9       5       7       11      42
55      S       12      3       5       10      38
56      S       13      9       9       9       42
57      S       4       6       1       10      34
58      S       13      8       13      1       48
REALLY struggling with this thanks!
59      S       6       4       7       9       51
60      S       12      3       5       13      33
61      S       6       6       7       9       44
62      S       11      4       11      7       48
63      S       14      4       15      7       49
64      S       8       2       9       5       33
65      S       5       3       6       8       45
66      S       8       3       4       6       42

The Binomial Distribution.

1. What makes the binomial distribution unique? What are its characteristics?

Give a real-world example of a distribution of data that would be considered binomial.

2. Solve the following problem:
About 30% of adults in United States have college degree.
(probability that a person has college degree is p = 0.30).

If N adults are randomly selected, find probabilities that

1) exactly X out of selected N adults have college degree
2) less than X out of selected N adults have college degree
3) greater than X out of selected N adults have college degree

Choose your numbers for N and X.

Student ID   Age   Gender   Nationality   Married   Children   Undergrad Major   GMAT Score   Previous salary   Monthly Expenses   School Debt
1   30   Male   US   No   0   Marketing   717   48100   1710   26580
2   32   Male   US   No   0   Finance   658   62600   1870   0
3   32   Female   US   No   0   Engineering   669   55500   1630   30560
4   30   Male   India   No   0   Marketing   687   45600   1430   0
5   39   Male   US   No   0   Marketing   633   59700   2020   25380
6   33   Male   US   No   0   Other non-business   658   70000   2610   0
7   30   Female   Europe   No   0   Other business   653   44500   1650   32370
8   35   Female   US   No   0   Engineering   784   54000   1930   33240
9   37   Female   Other   No   0   Engineering       40000   1640   64330
10   34   Male   US   Yes   0   Finance       72100   2670   39950
11   32   Female   US   No   0   Other business   784   42200   1130   9490
12   39   Male   US   Yes   2   Other non-business   627   69300   2320   70780
13   33   Female   US   Yes   1   Marketing   709   46100   2290   69360
14   26   Female   US   No   0   Finance   757   53100   1820   12490
15   35   Male   US   No   0   Finance   735   76400   1300   8840
16   35   Male   US   No   0   Marketing       67500   2230   26330
17   33   Male   US   No   1   Other non-business   686   67700   1770   48870
18   30   Male   India   No   0   Marketing       46700   1370   22690
19   29   Female   India   No   0   Marketing   749   46500   1530   20130
20   36   Female   US   Yes   1   Engineering   736   73700   1970   31150
21   36   Male   US   Yes   0   Finance   691   63400   1750   0
22   30   Male   South America   No   0   Marketing   698   51900   2550   33910
23   39   Male   India   No   0   Other non-business   743   63300   1750   29180
24   34   Male   US   Yes   1   Engineering   710   63200   2130   53280
25   40   Male   US   Yes   0   Other business   662   56200   2020   38560
26   30   Female   South America   Yes   0   Finance       43300   1240   26400
27   33   Male   US   Yes   1   Engineering       72200   1820   19450
28   32   Female   India   Yes   2   Engineering   718   44300   2600   68260
29   34   Male   US   No   0   Other non-business   716   59300   1620   0
30   40   Male   China   No   0   Finance   711   69100   2270   30460
31   37   Male   US   No   0   Engineering       76100   2430   0
32   28   Male   US   No   0   Marketing   743   58800   1540   35420
33   28   Male   US   No   0   Engineering   740   57200   1300   19180
34   27   Female   US   No   0   Finance   695   45000   2100   72220
35   31   Female   US   Yes   0   Other business       54200   1950   14640
36   35   Male   US   Yes   1   Other business       69500   2390   38330
37   30   Male   US   No   0   Engineering   765   77000   1450   16720
38   34   Female   China   No   0   Finance   770   47900   1970   39250
39   33   Male   US   Yes   1   Engineering       78900   1920   44820
40   34   Male   US   No   0   Other business   726   62300   2210   23620

1. Generate the 10 random samples of size 30 of School Debt variable. Find the mean and standard deviation of the each sample. Analyze the sample mean and standard deviation with the population mean and population standard deviation. In your workbook, rename the Sheet1 tab on the bottom of worksheet 1 to Random Sample of School Debt.

Three perfectly logical men are told to stand in a straight line, one in front of the other. A hat is put on each of their heads. Each of these hats was selected from a group of five hats: two identical black hats and three identical white hats. None of the men can see the hat on his own head, and they can only see the person's hat in front of him. In how many distributions of the hats can the person in front deduce his own hat color?