2. Return to decision you made when answering part D of Question 1.

A. If the alpha level had been .01 (or 1%) rather than .05 (or 5%), would your decision have been different? Please explain.

B. If the alpha level had been .10 (or 10%) rather than .05 (or 5%), would your decision have been different? Please explain.

3. Return again to Question 1. Suppose that rather than setting up a one-sided (or one-tailed) alternative hypothesis, you had set up a two-sided (or two-tailed) alterative hypothesis because you were not sure if the sample results would be greater than or less than the claimed population value. Would your p-value have been different if you had done this?  Please explain.

1. Suppose it is claimed that the typical adult travels an average distance of 16 miles to get to work each day. You believe this average is too low for Columbus residents. You survey a random sample of 98adults from Columbus and find that your sample travels an average distance of 17.6 miles to work each day, with a sample standard deviation of 7.8 miles.   Use this information to conduct the appropriate hypothesis test by going through the steps you learned about from our Chapter 22 and Chapter 23 lecture videos (and from your reading of Chapters 22 and 23). Assume the alpha level is .05 (or 5%).

A. What will the hypotheses be?

Ho:

Ha:

B. Use the following formula to compute the test statistic.

C. Based on what you see in Table B, what should the p-value be?

D. Will you reject or fail to reject the null hypothesis? Please state your decision and the reason why you are making that decision.

E. In general, if we end up rejecting the null hypothesis when conducting a hypothesis test, we say our results are _________________________ significant.

Suppose the given country road has large defects which are distributed along its length according to Poisson distribution with an average of 2 defects per mile. It takes the crew repairing these defects one full day to fix one of them. They move along the road and repair the defects as they are found. a) If the road is 10 miles long what is the probability they will be done in three weeks (15 working days)? b) What is the probability they will get at least to the middle of the road (i.e. advance by at least 5 miles) by the end of the second week (after 10 working days)? c) What is the mean and standard deviation of the length of the road they will cover by the end of the second week?

Q: An agronomist wanted to estimate the mean weight of a certain fruit (?) in his farm. He selected a random sample of size ? = 16, and found that the sample mean ?̅ = 55 gm and a sample stranded deviation ? = 3 gm. It is assumed that the population is normal with unknown standard deviation (?).

a) Find a point estimate for (?).

b) Find a 95% confidence interval for the population mean (?).

In a lottery game a player chooses four digits (digits can repeat, for instance 0, 2, 0, 2 is a valid choice) and bet $1 that all four of them will arise in the four digit number drawn from the lottery. It isn’t necessary that the order will be the same: if a player selects 2, 6, 7, 8 the selection of 8, 2, 7, 6 means he won. Player gets $200 if he wins.

1. What is the probability of winning?

2. What is the probability mass function of X, the net earnings in one game?

3. What are the mean and standard deviation of net earnings?

1. Slot machines are the favorite game at casinos throughout the U.S. The following sample data show the number of women and number of men who selected slot machines as their favorite game. Women Men Sample size 320 250 Favorite game-slots 256 165 Test at a 5% level of significance whether the difference between the proportion of women and proportion of men who say slots is their favorite game is statistically significant. (Please use both confidence interval approach and standard test statistic approach to solve the problem)

2. In a test of the quality of two television commercials, each commercial was shown in a separate test area six times over a one-week period. The following week a telephone survey was conducted to identify individuals who had seen the commercials. Those individuals were asked to state the primary message in the commercials. The following results were recorded. Commercial A Commercial B Number who saw commercial 150 200 Number who recalled message 63 60 Test at a 5% level of significance whether the difference between the recall proportions for the two populations is statistically significant. (Please use both confidence interval approach and standard test statistic approach to solve the problem)

A population is normally distributed with mean ? and standard deviation ?. Find the percentage of values which are between ?−2? and ?+2?.

An automobile dealer conducted a test to determine if the time in minutes needed to complete a minor engine tune-up depends on whether a computerized engine analyzer or an electronic analyzer is used. Because tune-up time varies among compact, intermediate, and full-sized cars, the three types of cars were used as blocks in the experiment. The data obtained follow.

Use α = 0.05 to test for any significant differences.

State the null and alternative hypotheses.

H₀: μ_Compact ≠ μ_Intermediate ≠ μ_Full-sized
H_a: μ_Compact = μ_Intermediate = μ_Full-sizedH₀: μ_Computerized ≠ μ_Electronic
H_a: μ_Computerized = μ_Electronic    H₀: μ_Compact = μ_Intermediate = μ_Full-sized
H_a: μ_Compact ≠ μ_Intermediate ≠ μ_Full-sizedH₀: μ_Computerized = μ_Electronic
H_a: μ_Computerized ≠ μ_ElectronicH₀: μ_Computerized = μ_Electronic = μ_Compact = μ_Intermediate = μ_Full-sized
H_a: Not all the population means are equal.

Find the value of the test statistic. (Round your answer to two decimal places.)

Find the p-value. (Round your answer to three decimal places.)

p-value =

State your conclusion.

Do not reject H₀. There is sufficient evidence to conclude that the mean tune-up times are not the same for both analyzers.Do not reject H₀. There is not sufficient evidence to conclude that the mean tune-up times are not the same for both analyzers.    Reject H₀. There is sufficient evidence to conclude that the mean tune-up times are not the same for both analyzers.Reject H₀. There is not sufficient evidence to conclude that the mean tune-up times are not the same for both analyzers.

A survey is given to 300 random SCSU students to determine their opinion of being a “Tobacco Free Campus.” Of the 300 students surveyed, 228 were in favor a tobacco free campus.

1. Find a 95% confidence interval for the proportion of all SCSU students in favor of a tobacco free campus.
2. Interpret the interval in part a.
3. Find the error bound of the interval in part a.
4. The Dean claims that at least 70% of all students are in favor of a tobacco free campus. Can you support the Dean’s claim at the 95% confidence level? Justify!

For any Hypothesis Test make sure to state Ho, Ha, Test statistic, p-value, whether you reject Ho, and your conclusion in the words of the claim. For any confidence interval make sure that you interpret the interval in context, in addition to using it for inference.

LINEAR ALGEBRA

The main topic studied is linear regression using matrices. The main idea being that you use a projection of the vector onto the subspace to find this linear regression equation.

QUESTION: Explain how you would use projections to find a quadratic regression for a given data, that is an equation of the kind y = ax2 + bx + c that best fits the data. This is just a theory question.

In randomized, double blind clinical trials of a new vaccine,Monkeys were randomly divided into two groups.Subjects in group x received the new vaccine while subject in group y received a control vaccine.After the first dose, 118 of 715 subjects in the experimental group ( group x) experienced fever as a side effect. After the first dose, 56 of 606 of the subjects in the control group ( group y ) experienced fever as a side effect.Construct a 90 % confidence interval for the diffence between the two population proportopm , Px-Py( Round to three decimal places as needed)

A shipment of 200 doses of an antibiotic has 7 defective doses.

    i) What is the probability that the 7^th dose out of the shipment will be defective?

   ii) If 5 doses are removed from the shipment what is the probability that none are defective?

   iii) If 5 doses are removed from the shipment what is the probability one dose is defective?

In a population of interest, we know that, 77% drink coffee, and 23% drink tea. Assume that drinking coffee and tea are disjoint events in this population. We also know coffee drinkers have a 30% chance of smoking. There is a 13% chance of smoking for those who drink tea.

1. Five individuals are randomly chosen from this population. What is the probability that four of them drink coffee?

2. Five individuals are randomly chosen from this population. What is the probability that the first four drink coffee and the last one drinks tea?

3. Five individuals are randomly chosen from this population. What is the expected number (population mean) of coffee drinkers?

4. Five individuals are randomly chosen from this population. Find the standard deviation for the number of coffee drinkers.

5. A person is randomly chosen from this population. What is the probability that the person smokes?

In November 2001, the Ag Globe Trotter newsletter reported that 90% of adults drink milk. A regional farmer’s organization planning a new marketing campaign across its multicounty area polls a random sample of 800 adults living there. In this sample 696 people said that they drink milk.

b. (4 points) At the 5% level, conduct a hypothesis test of the claim that 90% of adults drink milk. State the null and alternative hypothesis, calculate P-value and draw your conclusion clearly.

THIS PROBLEM NEEDS TO BE SOLVED ONLY USING EXCEL SOFTWARE!

1. Use the following data set to answer the following:

- Make a back to back stemplot (use https://www.learner.org/courses/againstallodds/interactives/stemplots.html click "go" under "plot your data mode" and then click "back to back datasets".

- Make side by side boxplots (use http://www.imathas.com/stattools/boxplot.html)

A) Is it appropoiate to use t-procedures to compare the mean DBH of trees in the north half of the tract with the mean DBH of the trees in the south half. Are conditions met? Check them.

B)Null hypothesis? alternative hypothesis? for comparing the two samples of tree DBHs? give reasons for your choices.

C) Perform a significance tesr. Report the test statistic, the dregress of freedom, and the p-value.

D) Find 95% confidence interval for the difference mean DBHs. Explain how this interval provides additional information about this problem.