A study identified top accounting firms across the United States. The Southeast and Gulf Coast regions reported the highest combined growths. A characteristic description of the accounting firms in the Southeast and Gulf Coast regions included the number of partners in the firm. Below represents the number of partners within various firms of the two regions [Southeast and Gulf Coast].

Southeast     174          Gulf Coast     79
Southeast     45            Gulf Coast     106
Southeast     29            Gulf Coast     22
Southeast     51            Gulf Coast     22
Southeast     40            Gulf Coast     38
Southeast     10            Gulf Coast     17
Southeast     29            Gulf Coast     27
Southeast     37            Gulf Coast     21
Southeast     32            Gulf Coast     17
Southeast     22            Gulf Coast     12
Southeast     9              Gulf Coast     9
Southeast     30            Gulf Coast     6
Southeast     21            Gulf Coast     9
                                       Gulf Coast     12
                                       Gulf Coast     18

(a)At the 0.05 level of significance, is there evidence of a difference in the variability in numbers of partners for Southeast region accounting firms and Gulf Coast accounting firms? (Include: null and alternate hypotheses, value of test statistic, decision rule, conclusion in a complete sentence that includes why in terms of the decision rule.)

(b) Interpret the p-value.

(c) What assumption do you have to make about the two populations in order to justify the use of the F test?

(d) Based on (a) and (b), which t test [Pooled Variance t-test or Separate Variance t-Test] should you use to test whether there is a significant difference in the mean number of partners for Southeast region accounting firms and Gulf Coast accounting firms?

1. a) Suppose average monthly sales for retail locations across the United States are approximately normally distributed with variance σ^2= 5200. We took a sample of size 50 and found ̄x= 12018,  Using this, conduct a hypothesis test with α= 0.05 to test the null hypothesis that the mean is 12000 vs. the alternative hypothesis that it is not. For full credit, state the null and alternative hypothesis, the test statistic, the rejection region, and your conclusion.

b)Using the setup from part a, if we know that the true mean is 12030, what is the probability of a type II error?

c)Using the setup from part a, what would be the p-value of this test? Would you reject the null hypothesis if α= 0.01? How about if α= 0.1

d)Using the set up from part a, perform the hypothesis test again, but now use the alternative hypothesis that the mean is actually greater than 12000.

e)Using the setup from part a, if we know the true mean is 12030 and we want the probability of a type I error to be 0.05 and the probability of a type II error

to be 0.10, what is the minimum sample size required to ensure this?

Almost all medical schools in the United States require students to take the Medical College Admission Test (MCAT). To estimate the mean score μ of those who took the MCAT on your campus, you will obtain the scores of an SRS of students. The scores follow a Normal distribution, and from published information you know that the standard deviation is 10.8 . Suppose that, unknown to you, the mean score of those taking the MCAT on your campus is 495 .

In answering the questions, use z‑scores rounded to two decimal places.

(a) If you choose one student at random, what is the probability that the student's score is between 490 and 500 ? Use Table A, or software to calculate your answer.

(Enter your answer rounded to four decimal places.)

probability:

(b) You sample 36 students. What is the standard deviation of the sampling distribution of their average score ¯x ? (Enter your answer rounded to two decimal places.)

standard deviation:

(c) What is the probability that the mean score of your sample is between 490 and 500 ? (Enter your answer rounded to four decimal places.)

probability:

Annual per capita consumption of milk is 21.6 gallons (Statistical Abstract of the United States: 2006). Being from the Midwest, you believe milk consumption is higher there and wish to support your opinion. A sample of 16 individuals from the midwestern town of Webster City showed a sample mean annual consumption of 24.1 gallons with a standard deviation of 4.8.

Compute the value of the test statistic. (Round to two decimal places)

What is the p-value? (Round to three decimal places).

At α=0.05, what is your conclusion?

1. a) Suppose average monthly sales for retail locations across the United States are approximately normally distributed with variance σ^2= 5200. We took a sample of size 50 and found ̄x= 12018,  Using this, conduct a hypothesis test with α= 0.05 to test the null hypothesis that the mean is 12000 vs. the alternative hypothesis that it is not. For full credit, state the null and alternative hypothesis, the test statistic, the rejection region, and your conclusion.

b)Using the setup from part a, if we know that the true mean is 12030, what is the probability of a type II error?

c)Using the setup from part a, what would be the p-value of this test? Would you reject the null hypothesis if α= 0.01? How about if α= 0.1

d)Using the set up from part a, perform the hypothesis test again, but now use the alternative hypothesis that the mean is actually greater than 12000.

e)Using the setup from part a, if we know the true mean is 12030 and we want the probability of a type I error to be 0.05 and the probability of a type II error

to be 0.10, what is the minimum sample size required to ensure this?

Should the U.S. Bring Back the Draft?

The United States has relied on an all-volunteer army since 1973, when the military draft was abolished. But at age 18, all American men are still required to register with the Selective Service, the federal agency responsible for implementing a draft. That’s in case the government decides that a draft is once again necessary to maintain America’s fighting force.

Is the U.S. better served by an all volunteer military or should everyone serve the country?

Remember Economist, the response should include the economic aspect of the question, such as:

• How benefits?
• What are some of the opportunity cost to the individuals?
• What are some of the opportunity cost to society?
• How would a draft affect the market in terms of supply and demand?
• Could a draft benefit GDP?

Please include topics related to your textbook whenever possible.

Almost all medical schools in the United States require students to take the Medical College Admission Test (MCAT). To estimate the mean score μ of those who took the MCAT on your campus, you will obtain the scores of an SRS of students. The scores follow a Normal distribution, and from published information you know that the standard deviation is 10.4 . Suppose that, unknown to you, the mean score of those taking the MCAT on your campus is 500 .

In answering the questions, use z‑scores rounded to two decimal places.

(a) If you choose one student at random, what is the probability that the student's score is between 495 and 505 ? Use  Table A, or software to calculate your answer.

(Enter your answer rounded to four decimal places.)

probability:

(b) You sample 25 students. What is the standard deviation of the sampling distribution of their average score ¯x ? (Enter your answer rounded to two decimal places.)

standard deviation:

(c) What is the probability that the mean score of your sample is between 495 and 505 ? (Enter your answer rounded to four decimal places.)

probability:

Almost all medical schools in the United States require students to take the Medical College Admission Test (MCAT). To estimate the mean score μ μ of those who took the MCAT on your campus, you will obtain the scores of an SRS of students. The scores follow a Normal distribution, and from published information you know that the standard deviation is 10.4 . Suppose that, unknown to you, the mean score of those taking the MCAT on your campus is 500 . In answering the questions, use z ‑scores rounded to two decimal places. (a) If you choose one student at random, what is the probability that the student's score is between 495 and505 ? Use Table A, or software to calculate your answer. (Enter your answer rounded to four decimal places.) probability: (b) You sample 25 students. What is the standard deviation of the sampling distribution of their average score x¯ ? (Enter your answer rounded to two decimal places.) standard deviation: (c) What is the probability that the mean score of your sample is between 495 and 505 ? (Enter your answer rounded to four decimal places.) probability:

Almost all medical schools in the United States require students to take the Medical College Admission Test (MCAT). To estimate the mean score ?μ of those who took the MCAT on your campus, you will obtain the scores of an SRS of students. The scores follow a Normal distribution, and from published information you know that the standard deviation is 10.810.8 . Suppose that, unknown to you, the mean score of those taking the MCAT on your campus is 495495 .

In answering the questions, use ?z‑scores rounded to two decimal places.

(a) If you choose one student at random, what is the probability that the student's score is between 490490 and 500500 ? UseTable A, or software to calculate your answer.

(Enter your answer rounded to four decimal places.)

probability:

(b) You sample 3636 students. What is the standard deviation of the sampling distribution of their average score ?¯x¯ ? (Enter your answer rounded to two decimal places.)

standard deviation:

(c) What is the probability that the mean score of your sample is between 490490 and 500500 ? (Enter your answer rounded to four decimal places.)