A retrospective study of 159 pairs of twins was performed. The twin pairs each had one male child and one female child. Their birth weights were studied to determine if the male twin was consistently heavier.

The difference in weights was calculated by subtracting the female weight (in ounces) from the male weight (in ounces):

d=xm-xf

After looking at 159 pairs of twins, the study finds the 99% confidence interval for the mean difference of weights (in ounces) is:

2.4 < μd < 6

Can we be reasonably sure that the male twins are heavier than the females?

• Yes
• No

Why or why not?

What kind of distribution would you expect the mean.median and mode to be equal?

If the distribution is symmetric, what measure of central tendency should you use?

If the distribution is skewed,what measure of central tendency should you use?

Explain intuitively why minimizing Type I error and maximizing the power of a test are contradic-

tory goals. Also draw the power function graph and label Type I error, Type II error, and power.)

Suppose two independent random samples of sizes n1 = 9 and n2 = 7 that have been taken from two normally distributed populations having variances σ12 and σ22 give sample variances of s12 = 94 and s22 = 13. (a) Test H0: σ12 = σ22 versus Ha: σ12 ≠ σ22 with σ = .05. What do you conclude? (Round your answers to 2 decimal places.) F = F.025 = H0:σ12 = σ22 (b) Test H0: σ12 < σ22versus Ha: σ12 > σ22 with σ = .05. What do you conclude? (Round your answers to 2 decimal places.) F = F.05 = H0: σ12 < σ22

Answer the following questions and use Excel to show your work.

A student has an important exam coming up and is contemplating not studying for the exam in order to attend a party with his friends. The student must earn a minimum score of 70% on the exam in order to successfully maintain his desired GPA. Suppose the student knows in advance that the exam will consist of 20 multiple-choice questions with 4 possible answers for each question. Answer questions 1–3 using the preceding information and modeling this situation as a binomial distribution.

1. What is the probability that the student will successfully earn exactly the required minimum score of 70% on the exam based solely on randomly guessing the correct answer for each question? a) 2.57 b) 2.57E-02 c) 2.57E-05 d) 2.57E-04

2. What is the probability that the student will earn less than the required minimum score of 70% on the exam based solely on randomly guessing the correct answer for each question? a) 0.74673 b) 0.85198 c) 0.99997 d) 0.23499

3. What is the probability that the student will successfully earn no less than the required minimum score of 70% on the exam based solely on randomly guessing the correct answer for each question? a) 3.51E-04 b) 2.95E-05 c) 6.87E-06 d) 1.27E-03

The tensile strength of a fiber used in manufacturing cloth is of interest to the purchaser. Previous experience indicates that the standard deviation of tensile strength is 2 psi. A random sample of eight fiber specimens is selected, and the average tensile strength is found to be 127 psi. USING MINITAB (please show all work)

(a) Test the hypothesis that the mean tensile strength equals 125 psi versus the alternative that the mean exceeds 125 psi. Use a = 0.05.

(b) What is the P-value for this test?

(c) Discuss why a one-sided alternative was chosen in part (a).

(d) Construct a 95% lower confidence interval on the mean tensile strength.

Answer the following questions and use Excel to show your work.

Customers arrive at a supermarket check-out counter with an average arrival rate of 9 customers per hour. Answer questions 8–10 using the preceding information and modeling this situation as a Poisson distribution.

8. What is the probability of less than 5 customers arriving at the supermarket check-out counter in a given 1-hour period? a) 0.054 b) 0.446 c) 0.359 d) 0.612

9. What is the probability of exactly 12 customers arriving at the supermarket check-out counter in a given 1-hour period? a) 0.262 b) 0.044 c) 0.073 d) 0.189

10. What is the probability of no less than 12 customers arriving at the supermarket check-out counter in a given 1-hour period? a) 0.115 b) 0.197 c) 0.381 d) 0.686

Post a clear and logical response in 150 to 200 words to the following questions/prompts, providing specific examples to support your answers.

Think about examples of how using probability distribution could affect ethics. What are the ethical concerns with capitalizing using probability distribution techniques? Provide an example of using probability distribution techniques.

A bank classifies borrowers as "high risk" or "low risk," and 23% of its loans are made to those in the "high risk" category. Of all the bank's loans, 8% are in default. It is also known that 46% of the loans in default are to high-risk borrowers. Let H represent the event that a randomly selected loan is issued to a "high risk" borrower. Let D be the event that a randomly selected loan is in default. Round your answers to 4 decimal places. Your work for this entire problem will be hand-graded, see instructions below.

a. What is the probability that a randomly selected loan is in default and issued to a high-risk borrower?

b. What is the probability that a loan will default, given that it is issued to a high-risk borrower?

c. What is the probability that a randomly selected loan is either in default or issued to a high-risk borrower?

d. A loan is being issued to a borrower who is not high-risk. What is the probability that this loan will default?

e. Are events D and H independent? Justify the answer.
Yes, because P(D) ≠ P(H)
Yes, because P(H | D) > P(H) + P(D)
No, because P(D ∩ H) ≠ P(D) × P(H)
No, because P(D | H) ≠ P(H)
Not enough information to determine

In 2011, when the Gallup organization polled investors, 31% rated gold the best long-term investment. But in April of 2013 Gallup surveyed a random sample of U.S. adults. Respondents were asked to select the best long-term investment from a list of possibilities. Only 238 of the 950 respondents chose gold as the best long-term investment. By contrast, only 92 chose bonds.

a. Compute the standard error for each sample proportion. Compute and describe a 95% confidence interval in the context of the question.

b. Do you think opinions about the value of gold as a long-term investment have really changed from the old 31% favorability rate, or do you think this is just sample variability? Explain.

c. Suppose we want to increase the margin of error to 5%, what is the necessary sample size?

d. Based on the sample size obtained in part c, suppose 112 respondents chose gold as the best long-term investment. Compute the standard error for choosing gold as the best long-term investment. Compute and describe a 95% confidence interval in the context of the question.

e. Based on the results of part d, do you think opinions about the value of gold as a long-term investment have really changed from the old 31% favorability rate, or do you think this is just sample variability? Explain.

The computer operations department had a business objective of reducing the amount of time to fully update each subscriber's set of messages in a special secured email system. An experiment was conducted in which 23 subscribers were selected and three different messaging systems were used. Eight subscribers were assigned to each system, and the update times were measured as follows:

Given Sample Means: x̅a = 41.46, x̅b = 36.33, x̅c = 35.84, Grand Mean = 38.29

Given Sample Standard Deviations: sa = 4.32, sb = 4.00, sc = 3.02, S = 4.34

A) At the 0.05 level of significance, is there evidence of a difference in the variance of the update times between Systems B and C? (Show your work: hypotheses, test statistic, critical value, and decision).

B) Fill out the following summary table for One-Way ANOVA:

C) Using the Tukey-Kramer method, determine which pair of the designs have the difference in mean distances at the 0.05 level of significance by filling out the following table (the upper-tail critical value from the studentized range distribution with 3 and 20 degrees of freedom as Qα = 3.578)

Please do not use this as an example: Suppose a company printed baseball cards. It claimed that 30% of its cards were rookies; 60% were veterans but not All-Stars; and 10% were veteran All-Stars.

When evaluating a chi-square test, describe the importance of the goodness of fit test. Provide an example and explain how the test is used to evaluate the data.

Cholesterol levels for a group of women aged 30-39 follow an approximately normal distribution with mean 190.14 milligrams per deciliter (mg/dl). Medical guidelines state that women with cholesterol levels above 240 mg/dl are considered to have high cholesterol and about 9.3% of women fall into this category.

1. What is the Z-score that corresponds to the top 9.3% (or the 90.7-th percentile) of the standard normal distribution? Round your answer to three decimal places.

2. Find the standard deviation of the distribution in the situation stated above. Round your answer to 1 decimal place.

3. For each dataset, what is the unit of observation? What is/are the variable(s) collected? State whether the distribution of this data will be skewed and explain why. Draw a plausible sketch of the distribution and label the axes.

a. Lengths of pant legs cut and sewn to be 32 inches long.

b. The times for students in an introductory psychology course to complete a difficult one-hour timed exam.

A drug study compared the amounts of nitrate absorbed into the skin for brand name and generic formulations of the drug. The two drugs were both applied to the arms of 14 participants, and the amounts absorbed, in mg/cm³, were measured. Does the mean amount absorbed differ between the generic and brand name drug? Use formal hypothesis testing.