In SAS code please.

Tennis balls are tested in a machine to show how many bounces they can withstand before they fail to bounce 30% of their dropping height. Two brands of balls (W and P) are compared. In addition, the effect of shelf life on these brands is tested. Half of the balls of each brand are 6 months old, the other half, fresh. Using a two-way analysis of variance, what conclusions can you reach? The data are shown below:

Brand W (New): 67 72 74 82 81

Brand P (New): 75 76 80 72 73

Brand W (Old): 46 44 45 51 43

Brand P (Old): 63 62 66 62 60

the Consumer Reports National Research Center conducted a telephone survey of 2,000 adults to learn about the major economic concerns for the future. The survey results showed that 1,700 of the respondents think the future health of Social Security is a major economic concern. If computing the confidence intervals manually, make sure to use at least three decimal digits for the critical values.

a. What is the point estimate of the population proportion of adults who think the future health of Social Security is a major economic concern?

b. At 90% confidence, what is the margin of error (to 4 decimals)?

c. Develop a 90% confidence interval for the population proportion of adults who think the future health of Social Security is a major economic concern (to 3 decimals).

d. Develop a 95% confidence interval for this population proportion (to 3 decimals).

PYTHON: The following puzzle is known as The Big Cross-Out Swindle.“Beginning with the word ‘NAISNIENLGELTETWEORRSD,’ cross out nine letters in such a way that the remaining letters spell a single word”. Write a program that creates variables named startingWord, crossedOutLetters, andremainingLetters. The program should assign to startingWord the string given in the puzzle, assign tocrossedOutLetters a list containing every other letter of startingWordbeginning with the initial letter N, and assign to remainingLetters a list containing every other letter of startingWord beginning with the second letter, A. The program should then display the values of the three variables.

In a survey of 3316 ​adults, 1433 say they have started paying bills online in the last year. Construct a​ 99% confidence interval for the population proportion. Interpret the results.

(a) A​ 99% confidence interval for the population proportion is ( ),( ).

​(Round to three decimal places as​ needed.)

(b) Interpret your results. Choose the correct answer below:

1. With​ 99% confidence, it can be said that the population proportion of adults who say they have started paying bills online in the last year is between the endpoints of the given confidence interval.

2. The endpoints of the given confidence interval show that adults pay bills online​ 99% of the time.

3. With​ 99% confidence, it can be said that the sample proportion of adults who say they have started paying bills online in the last year is between the endpoints of the given confidence interval.

1. To find the optimal solution to a linear optimization problem, do you have to examine all the points in the feasible region? Explain.

2. Can a linear programming problem have no solution? More than one solution? Explain.

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3. A beverage can manufacturer makes three sizes of soft drink cans—Small, Medium and Large. Production is limited by machine availability, with a combined maximum of 90 production hours per day, and the daily supply of metal, no more than 120 kg per day. The following table provides the details of the input needed to manufacture one batch of 100 cans for each size.

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Develop a linear programming model to maximize profit and determine how many batches of each can size should be produced.

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4. Gatson manufacturing company produces two types of tires: Economy tires and Premium tires. The manufacturing time and the profit contribution per tire are given in the following table.

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Answer the following assuming that the company is interested in maximizing the total profit contribution.

1. What is the linear programming model for this problem?
2. Develop a spreadsheet model and find the optimal solution using Excel Solver. How many tires of each model should Gatson manufacture?
3. What is the total profit contribution Gatson can earn with the optimal production quantities?

1. A researcher is testing the claim that adults consume an average of at least 1.85 cups of coffee per day. A sample of 35 adults shows a sample mean of 1.70 cups per day with a sample standard deviation of 0.4 cups per day. Test the claim at a 5% level of significance. What is your conclusion?

2. A government Bureau claims that more than 50% of U.S. tax returns were filed electronically last year. A random sample of 150 tax returns for last year contained 86 that were filed electronically. Test the Bureau's claim at a 5% level of significance. What is your conclusion? Report the p-value for this test.

3. A major automobile company claims that its New electric-powered car has an average range of more than 100 miles. A random sample of 50 new electric cars was selected to test the claim. Assume that the population standard deviation is 12 miles. A 5% level of significance will be used for the test.

   A) What would be the consequences of making a Type II error in this problem?

   B) Compute the Probability of making a Type II error if the true population means is 105 miles.

   C) What is the maximum probability of making a Type I error in this problem?

Please Note: A hypothesis test answer must contain: a Null and an Alternate Hypothesis, a computed value of the test statistic, a critical value of the test statistic, a Decision, and a Conclusion.

The following data represent crime rates per 1000 population for a random sample of 46 Denver neighborhoods.†

(a) Use a calculator with mean and sample standard deviation keys to find the sample mean x and sample standard deviation s. (Round your answers to one decimal place.)

(b) Let us say the preceding data are representative of the population crime rates in Denver neighborhoods. Compute an 80% confidence interval for μ, the population mean crime rate for all Denver neighborhoods. (Round your answers to one decimal place.)

(c) Suppose you are advising the police department about police patrol assignments. One neighborhood has a crime rate of 62 crimes per 1000 population. Do you think that this rate is below the average population crime rate and that fewer patrols could safely be assigned to this neighborhood? Use the confidence interval to justify your answer.

Yes. The confidence interval indicates that this crime rate is below the average population crime rate.Yes. The confidence interval indicates that this crime rate does not differ from the average population crime rate.    No. The confidence interval indicates that this crime rate is below the average population crime rate.No. The confidence interval indicates that this crime rate does not differ from the average population crime rate.

(d) Another neighborhood has a crime rate of 75 crimes per 1000 population. Does this crime rate seem to be higher than the population average? Would you recommend assigning more patrols to this neighborhood? Use the confidence interval to justify your answer.

Yes. The confidence interval indicates that this crime rate does not differ from the average population crime rate.Yes. The confidence interval indicates that this crime rate is higher than the average population crime rate.    No. The confidence interval indicates that this crime rate is higher than the average population crime rate.No. The confidence interval indicates that this crime rate does not differ from the average population crime rate.

(e) Compute a 95% confidence interval for μ, the population mean crime rate for all Denver neighborhoods. (Round your answers to one decimal place.)

(f) Suppose you are advising the police department about police patrol assignments. One neighborhood has a crime rate of 62 crimes per 1000 population. Do you think that this rate is below the average population crime rate and that fewer patrols could safely be assigned to this neighborhood? Use the confidence interval to justify your answer.

Yes. The confidence interval indicates that this crime rate is below the average population crime rate.Yes. The confidence interval indicates that this crime rate does not differ from the average population crime rate.    No. The confidence interval indicates that this crime rate is below the average population crime rate.No. The confidence interval indicates that this crime rate does not differ from the average population crime rate.

(g) Another neighborhood has a crime rate of 75 crimes per 1000 population. Does this crime rate seem to be higher than the population average? Would you recommend assigning more patrols to this neighborhood? Use the confidence interval to justify your answer.

Yes. The confidence interval indicates that this crime rate does not differ from the average population crime rate.Yes. The confidence interval indicates that this crime rate is higher than the average population crime rate.    No. The confidence interval indicates that this crime rate is higher than the average population crime rate.No. The confidence interval indicates that this crime rate does not differ from the average population crime rate.

(h) In previous problems, we assumed the x distribution was normal or approximately normal. Do we need to make such an assumption in this problem? Why or why not? Hint: Use the central limit theorem.

Yes. According to the central limit theorem, when n ≥ 30, the x distribution is approximately normal.Yes. According to the central limit theorem, when n ≤ 30, the x distribution is approximately normal.    No. According to the central limit theorem, when n ≥ 30, the x distribution is approximately normal.No. According to the central limit theorem, when n ≤ 30, the x distribution is approximately normal.

Students are classified according to religious preference (Buddhist, Jewish,

Protestant, Roman Catholic, or Other) and political affiliation (Democrat, Republican,

Independent, or Other).

RELIGIOUS PREFERENCE AND POLITICAL AFFILIATION

RELIGIOUS PREFERENCE

POLITICAL

AFFILIATION BUDDHIST JEWISH PROTESTANT ROM. CATH. OTHER TOTAL

Democrat 30 30 40 60 40 200

Republican 10 10 40 20 20 100

Independent 10 10 20 20 40 100

Other 0 0 0 0 100 100

Total 50 50 100 100 200 500

(a) Is anything suspicious about these observed frequencies?

(b) Using the .05 level of significance, test the null hypothesis that these two variables

are independent.

(c) If appropriate, estimate the effect size

A card is drawn at random from a deck of cards. What is the probability that

(a) it is a heart, given that it is red?

(b) it is higher than a 10, given that it is a heart? (Interpret J, Q, K, A as 11, 12, 13, 14.)

(c) it is a jack, given that it is red?

In answering the question(s), make sure to write down the following 7 steps.

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.

1. 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

2. 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

The Wall Street Journal reported that 33% of taxpayers with adjusted gross incomes between $30,000 and $60,000 itemized deductions on their federal income tax return. The mean amount of deductions for this population of taxpayers was $15,968. Assume that the standard deviation is $2,190. Use z-table.

a. What is the probability that a sample of taxpayers from this income group who have itemized deductions will show a sample mean within $184 of the population mean for each of the following sample sizes: 30, 50, 100, and 400? Round your answers to four decimals.

b. What is the advantage of a larger sample size when attempting to estimate the population mean? Round your answers to four decimals.

A larger sample (Select your answer -increases or decreases) the probability that the sample mean will be within a specified distance of the population mean. In the automobile insurance example, the probability of being within +/-184 of u ranges from (blank) for a sample of size 30, to (blank) for a sample of size 400.

The variance in a production process is an important measure of the quality of the process. A large variance often signals an opportunity for improvement in the process by finding ways to reduce the process variance. The following sample data show the weight of bags (in pounds) produced on two machines: machine 1 and 2.

m1 = (2.95, 3.45, 3.50, 3.75, 3.48, 3.26, 3.33, 3.20, 3.16, 3.20, 3.22, 3.38, 3.90, 3.36, 3.25, 3.28, 3.20, 3.22, 2.98, 3.45, 3.70, 3.34, 3.18, 3.35, 3.12)

m2 = (3.22, 3.30, 3.34, 3.28, 3.29, 3.25, 3.30, 3.27, 3.38, 3.34, 3.35, 3.19, 3.35, 3.05, 3.36, 3.28, 3.30, 3.28, 3.30, 3.20, 3.16, 3.33)

A) Provide descriptive statistical summaries of the data for each model; in particular, the sample variance and the sample size for each machine.

Please copy your R code and the result and paste them here.

B) Conduct a statistical test to determine whether there is a significant difference between the variances in the bag weights for two machines. First, clearly formulating your hypotheses below.

C) Compute the test statistic.

Please copy your R code and the result and paste them here.

D) Compute the p value.

Please copy your R code and the result and paste them here.

E) Use a .05 level of significance to compute both critical values for your test statistic.

Please copy your R code and the result and paste them here

F) Use a .05 level of significance. What is your conclusion?

G) Use the function var.test() in R to run the test directly to confirm your results above are correct.

Please copy your R code and the result and paste them here.

H) Construct a 95% confidence interval for the variance of the weight of bags produced on machine 1.

Please copy your R code and the result and paste them here.

I) Construct a 95% confidence interval for the standard deviation of the weight of bags produced on machine 2.

Please copy your R code and the result and paste them here.

J) Which machine, if either, provides the greater opportunity for quality improvements?

A business school claims that students who complete a 3-month typing course can type a mean of more than 1200 words an hour. A random sample of 25 students who completed this course typed a mean of 1125 words an hour, with a standard deviation of 85 words. Assume that typing speeds for all students who complete this course have an approximately normal distribution. A) Using the P-Value method and a significance level of 1%, is there evidence to support the business school’s claim? B) Construct the corresponding confidence interval and explain how it supports your conclusion in (a).

We toss a fair 6 sided die and flip a fair coin twice. Define the random variable Y1 to be the number of sports atop the die. Define Y2 to be the total number of heads obtained on the two flips of the coin.

a) Find the mean value and standard deviation of Y1.

b) Find the mean value and standard deviation of Y2.

c) Find the mean value and standard deviation of Y1+Y2.

d) What are the mean value and standard deviation of 5+Y1?

e) What are the mean value and standard deviation of 5(Y1)?