A major oil company has developed a new gasoline additive that is supposed to increase mileage. To test this hypothesis, ten cars are randomly selected. The cars are driven both with and without the additive. The results are displayed in the following table. Can it be concluded, from the data, that the gasoline additive does significantly increase mileage?

Let d=(gas mileage with additive)−(gas mileage without additive). Use a significance level of α=0.05 for the test. Assume that the gas mileages are normally distributed for the population of all cars both with and without the additive.

Step 1 of 5: State the null and alternative hypotheses for the test.

Step 2 of 5: Find the value of the standard deviation of the paired differences. Round your answer to two decimal places.

Step 3 of 5: Compute the value of the test statistic. Round your answer to three decimal places

Step 4 of 5: Determine the decision rule for rejecting the null hypothesis H0H0. Round the numerical portion of your answer to three decimal places.

Step 5 of 5: Make the decision for the hypothesis test.

A developmental psychologist would like to know whether there is a difference in the sociability scores of children according to the number of siblings they have. He chose three random samples of n = 5 children each according to three groups and measured their level of sociability using a standardized test. The scores are shown in the table below. Do the scores indicate significant differences among the three groups?

a. Using the 5 steps of hypothesis testing, test at α .05. (15 pts)

b. Conduct two post hoc tests, Tukey’s HSD Test and the Scheffe Test, both at α .05, and compare your answers. (9 pts)

Need help with the ten step by hand ANOVA ... specifically the sum of squres/between/within calculations in the hypothesis testing

and the steps associated with the post hoc tests

Thank you!!

Consider two stocks with returns RA and RB with the following properties. RA takes values -10 and +20 with probabilities 1/2. RB takes value -20 with probability 1/3 and +50 with probability 2/3. Corr(RA,RB) = r (some number between -1 and 1). Answer the following questions

(a) Express Cov(RA,RB) as a function of r

(b) Calculate the expected return of a portfolio that contains share α of stock A and share 1−α of stock B. Your answer should be a function of α (c) Calculate the variance of the portfolio from part B (Hint: returns are now potentially dependent)

(d) What value of α* minimizes the variance of the portfolio? Your answer should be a function of r, denoted by α*(r).

(e) For what range of values for r is your α*(r) 6 1? What is the solution to the above problem if r is outside of that range? (Hint: draw a graph and find α* ∈ [0,1] that minimizes variance) (f) Is α*(r) increasing or decreading? (Hint: take the derivative with respect to r)

(g) Which r wouldtheinvestorprefertohave, positiveornegative? Whatistheintuition for that result? 3

7. Hunting :

The probability that an eagle kills a rabbit in a day of hunting is 10%. Assume that results are independent for each day.

(a) Write the probability mass function for the number of days until a successful hunt.

(b) What is the probability that the first successful hunt occurs on day five?

(c) What is the expected number of days until a successful hunt?

(d) If the eagle can survive up to 10 days without food (it requires a successful hunt on the 10th day), what is the probability that the eagle is still alive 10 days from now?

Hogg's Probability and Statistical Inference (9th Edition) - Problem 1.4-20E - How is this problem solved?

Hunters A & B shoot at a target with probabilities of p1 and p2, respectively. Assuming independence, can p1 and p2 be selected so that P(zero hits)=P(one hit)=P(two hits)?

A national organization that promotes good local government management (ICMA) is interested if a city’s region is related to privatized waste collection.

Privatized                     Government
EAST 20                                40

WEST 10                               30

SOUTH 30                             40

1. Provide null and alternative hypotheses in formal terms and layperson's terms for the chi-square two sample test.

2. Do the math and reject/accept at a=.05

3. Explain the results in layperson's terms

The local library if they get more patrons visiting by shifting some early morning hours to evening. They take a sample of days with morning hours included 8-5pm compared to 12-9pm.

8am-5pm hours: 50, 40, 60, 60, 70, 35, 40

12-9 PM hours : 40, 80, 70, 60, 85, 90, 70

1. Provide null and alternative hypotheses in formal terms and layperson's terms for the t test for independent samples

2. Do the math and reject or accept at a=.05

3. Explain the results in layperson's terms

4. Calculate and explain a 95% confidence interval in layperson's terms if appropriate.

The library thinks the average number of patrons for 12-9 PM hours is 60. Use the data for 12-9 from the previous question

1. Provide the null and alternative hypotheses formal and layperson’s informal terms for a t one-sample test.

2. Do the math and reject or accept at a=0.05

3. Explain the results in layperson’s terms

An engineer at a microcircuit factory will inspect a batch of silicon wafers to try to find defects. Assume that there are four defective integrated circuits in a container containing twenty wafers. For that inspection two random wafers are selected. Calculate the probability that:
a) None of them have defects
b) At least one of the two has no defects.

Consider the following sample data for the relationship between advertising budget and sales for Product A: Observation 1 2 3 4 5 6 7 8 9 10

Advertising ($) 60,000 70,000 70,000 80,000 80,000 90,000 100,000 100,000 110,000 110,000

Sales ($) 363,000 432,000 417,000 502,000 483,000 537,000 614,000 625,000 653,000 666,000

What is the slope of the "least-squares" best-fit regression line? Please round your answer to the nearest hundredth.

How many even 4-digit numbers can be formed from the digits 1, 2, 3, 6, and 9 with no repetitions allowed? (Hint: Try filling the units place first.)

#%Last, the researchers hopes to understand how GDP influence birth rates. They theorize that perhaps countries with higher gross domestic product will invest more in women’s schooling. If more women know how to read, they hypothesize, then those women may have fewer children (due to better birth control knowledge, higher career aspirations, etc). The researchers add a variable measuring the percentage of women who can read to the regression equation. The results are presented in Equation 3 of Table 1.

Table 1. OLS Regression Coefficients Representing Influence of Economic Output (GDP) and Control Variables on Total Fertility Rate

(Significance level in parentheses)

Question 1 What conclusion should the researcher draw about the focal relationship when comparing Equation 3 to Equation 2? (For this question, you should reference specific numbers that you are using to draw your conclusion.)

#$Last, the researchers hopes to understand how GDP influence birth rates. They theorize that perhaps countries with higher gross domestic product will invest more in women’s schooling. If more women know how to read, they hypothesize, then those women may have fewer children (due to better birth control knowledge, higher career aspirations, etc). The researchers add a variable measuring the percentage of women who can read to the regression equation. The results are presented in Equation 3 of Table 1.

Question 1. What is the reason the researchers are adding the variable measuring female literacy?

Question 2. Clearly explain which elaboration strategy the researchers are using when they add the new variable. You may draw a picture on your worksheet. You should not reference any numbers from the equation in answering this question

Only look at equation 3!!

Table 1. OLS Regression Coefficients Representing Influence of Economic Output (GDP) and Control Variables on Total Fertility Rate

(Significance level in parentheses)

Explain what a meta-analysis is (i.e., what is a meta-analysis in terms of effect sizes).

A bag contains 3 white chips and 3 red chips. you repeatedly draw a chip at random from the bag. if it's white, you set it aside; if it's red, you put it back in the bag. after removing all 3 white chips, you stop. what is the expected number of times you will draw from the bag?

"Tongue Piercing May Speed Tooth Loss, Researchers Say" is the headline of an article. The article describes a study of 51 young adults with pierced tongues. The researchers found receding gums, which can lead to tooth loss, in 16 of the participants.

(a) Construct a 95% confidence interval for the proportion of young adults with pierced tongues who have receding gums. (Round your answers to three decimal places.)

( , )

(b) What assumptions must be made for use of the z confidence interval to be appropriate? (Select all that apply.)

1) The sample is voluntary.

2) The sample is a random sample.

3) The sample is independent.

4) The sample size is large.