1. Use excel function exp( ) to calculate raising e to the power of (-2.5 + 2*X1 + 3*X2), where X1=5.6 and X2=3.

2. Denote the result from part 1 as Y, calculate the Y/(1+Y), and let us denote this ratio as prob, i.e., prob= Y/(1+Y). Demonstrate the quantity is sandwiched by this interval (0, 1) by trying different values of X1 and X2. Also realize the any quantity that is capped between 0 and 1 can lend itself to the interpretation of probability.

3. Use excel function ln() to calculate ln(67).

The following sample observations were randomly selected. X: 5 6 2 7 11 Y: 3 6 4 6 6 (a) Determine the 0.90 confidence interval for the mean predicted when X = 7. (Do not round the intermediate values. Round your answers to 3 decimal places.)

What is Confidence interval_____

(b) Determine the 0.90 prediction interval for an individual predicted when X = 7. (Do not round the intermediate values. Round your answers to 3 decimal places.) What is Prediction interval_____

Let S denote the 10-element set {a,b,c,d,e,f,g,h,i,j}. How many ways can we construct a subset of S of size 7 ? 120 How many ways can we construct a subset of S of size 7 containing the element j? 84 How many ways can we construct a subset of S of size 7 containing i but not j ? 28 How many ways can we construct a subset of S of size 7 containing h but neither i nor j ? 7 How many ways can we construct a subset of S of size 7 containing g but not h, i or j? 1 Note that every subset of S of size 7 falls into exactly one of the categories described in parts (b) through (e) above. Use that fact to derive a summation formula involving expressions nCr.

Suppose researchers interested in the effects of adolescent exposure to mold in a household is associated with asthma. Researchers collected information about a sample of children living in homes determined to have a significant amount of potential mold exposure and determined that 154 out of the 213 children had asthma. After a sample of 428 households with not a sufficient amount of mold exposure, only 108 children were found to have asthma. A) Conduct a statistical test to determine if there is a significant risk difference for asthma based on exposure to mold at the alpha level of 0.05. B) Construct a confidence interval about your point estimate for the difference in risk between the groups.

a. Find the mean, standard deviation, and five number summaries for each type of M&M (plain and peanut) for the number of M&Ms in each bag.

b. Use the information found in Step 1 to draw side by side boxplots, comparing the number of M&Ms in each bag of plain and peanut M&Ms. Discuss the shape of each.

c. Write a summary paragraph about your data. Make at least 4 different observations about your data and/or boxplots using your statistical knowledge.

Plain M&M:

(14, 14, 15, 16, 15, 14, 16, 15, 13, 14, 14, 14, 14, 14, 14, 15, 14, 16, 14, 14, 15, 16, 14, 15, 11, 15, 15, 15, 13, 15, 13, 16, 14, 14, 14, 15, 14, 15, 15, 14, 15, 15, 15, 14, 16, 13)

Peanut M&M:

(8, 8, 7, 6, 8, 7, 7, 8, 7, 6, 6, 7, 7, 7, 7, 8, 7, 8, 9, 7, 7, 8, 7, 7, 6, 7, 7, 8, 7, 7, 7, 7, 7, 6, 7, 8, 7, 7, 7, 5, 7, 7, 7, 7, 8, 7, 7, 8, 7, 7)

You are studying the market value of home in Houston. You collect data from the recent sale of 30 single family homes. The data is organized and stored in an Excel file. The dataset includes the fair market value (in $thousands), land area of the property in acres, and age, in years of the 30 homes. Develop a multilinear regression model to predict the fair market value based on land area of the property (in acres) and age, in years.

The name of the Excel data file is HoustonHomes.xlsx. Import the data into SPSS and complete the assignment using SPSS.

1. State the multiple regression equation.

2. Interpret the meaning of the slopes, b1 and b2 , in this problem?

3. Explain why the regression coefficient, b0, has no practical meaning in the context of this problem.

4. Predict the mean fair market value for a house that has a land area of 0.25 acre and is 55 years old?

5. Construct a 95% prediction interval estimate for the fair market value for an individual house that has a land area of 0.25 acre and is 55 years old.

Do you typically stop or speed up at a yellow traffic light?

Ho: proportion who speed up = 0.70 Ha: proportion who speed up ≠ 0.70

Average: .4375  Standard Deviation: .4961

The sample size is 32 and our focus is who does speed up at the yellow light.

How many speeding tickets have you had in your life?

Ho: average tickets = 5 Ha: average tickets ≠ 5

Average: 7.03 Standard Deviation: 10.00

Test the hypotheses and include a full calculation of the test statistic, p-value, and state the full conclusion in words for both problems. Show all work.

In a test of weight loss​ programs, 160 subjects were divided such that 32 subjects followed each of 5 diets. Each was weighed a year after starting the diet and the results are in the ANOVA table below. Use a 0.025 significance level to test the claim that the mean weight loss is the same for the different diets.

Should the null hypothesis that all the diets have the same mean weight loss be​ rejected?

A.

YesYes​,

because the​ P-value is

greater thangreater than

the significance level.

B.

YesYes​,

because the​ P-value is

less thanless than

the significance level.

C.

NoNo​,

because the​ P-value is

less thanless than

the significance level.

D.

NoNo​,

because the​ P-value is

greater thangreater than

the significance level.

A small regional carrier accepted 20 reservations for a particular flight with 17 seats. 13 reservations went to regular customers who will arrive for the flight. Each of the remaining passengers will arrive for the flight with a 40% chance, independently of each other.
Find the probability that overbooking occurs.
Find the probability that the flight has empty seats.

Assume that a procedure yields a binomial distribution with a trial repeated n=5n=5 times. Use some form of technology to find the probability distribution given the probability p=0.299p=0.299 of success on a single trial.
(Report answers accurate to 4 decimal places.)

Are America's top chief executive officers (CEOs) really worth all that money? One way to answer this question is to look at row B, the annual company percentage increase in revenue, versus row A, the CEO's annual percentage salary increase in that same company. Suppose that a random sample of companies yielded the following data:

​

Do these data indicate that the population mean percentage increase in corporate revenue (row B) is different from the population mean percentage increase in CEO salary? Assume that the distribution of differences is approximately normal, mound-shaped and symmetric. Use a 5% level of significance. What is the alternate hypothesis?

​

The Gravy Company has decided to launch a new advertisement campaign in grocery stores to promote their products. The idea is to put small signs in the meat section (next to the Turkey, Ham, etc.) which read, "Get on board to the gravy train! The company wonders whether the different groups of consumers who eat different meats also have different gravy preferences. The table below is from a random sample of college students. The row denotes whether the student's family has gravy at Thanksgiving or not. The column denotes the type of meat served.

Formulate a set of hypotheses to test whether the two variables are independent or dependent and perform the test.

To test whether extracurricular activity is a good predictor of college success, a college administrator records whether students participated in extracurricular activities during high school and their subsequent college freshman GPA.

(a) Code the dichotomous variable and then compute a point-biserial correlation coefficient. (Round your answer to three decimal places.)


(b) Using a two-tailed test at a 0.05 level of significance, state the decision to retain or reject the null hypothesis. Hint: You must first convert r to a t-statistic.

Retain the null hypothesis OR Reject the null hypothesis.