Refer to Section 6-5b - Styles of Leadership In your own words, compare and contrast the pros and cons of Autocratic, Participative, and Entrepreneurial leadership styles. Which leadership style would you most enjoy working under? Which leadership style most reflects your style as a leader? Do you have any stories or thoughts from experiences working under a leader that was very Autocratic, Participative, or Entrepreneurial? Did it change your outlook on this type of leadership style?

Discuss your position on the following concerning Section 936 of the Internal Revenue Code: The 936 companies were criticized for arguing that they only defended their tax benefits without supporting local development as a research and high-tech center.

The mean of the population (µ) on a test that measures math skills of middle school students is 200. The variance  is 100. The test scores for the students in Mr. Petris’s class at Suburban Middle School are given below.

195        203        200               193        207               201        199               197        203               199       

195        220        200               202        200               193        205               187        218               189       

173        209        190               190        206               209        185               179        188               205

Use a rejection region with a statistical significance of 5% (p<.05) only in the upper tail.

1. What is the name of the z-test you will conduct?
2. What would be an appropriate null hypothesis that you could test using the provided information?
3. What should you conclude about the null hypothesis you developed (reject or fail to reject)? Explain.

Now use a rejection region with a total statistical significance of 5% (p<.05) incorporated in both the upper and lower tails.

4. What is the name of the z-test you will conduct?
5. What would be an appropriate null hypothesis that you could test using the provided information?
6. What should you conclude about the null hypothesis you developed (reject or fail to reject)? Explain.

From the section above, you should have found that dSres = - dUsys/Tsys This expression relates the
change in entropy of the system to the change in internal energy of the system, and the
temperature shared by system and reservoir.

B. Recall the relationship between entropy and multiplicity, S = k ln Ω.

Use this to describe the quantity dSuniv in terms of multiplicities.

Use the relationship between entropy and multiplicity to derive an expression for the ratio Ωf/Ωi for such an energy transfer.

If the energy of the system increases, what happens to the entropy of the reservoir?

If the energy of the system increases, what happens to the multiplicity of the reservoir?

1. Waiting time for checkout line at two stores of a supermarket chain were measured for a random sample of customers at each store. The chain wants to use this data to test the research (alternative) hypothesis that the mean waiting time for checkout at Store 1 is lower than that of Store 2. (12 points)

1. What are the null and alternative hypothesis for this research?
2. What are the sample mean waiting time for checkout line and the sample standard deviation for the two stores?
3. Compute the test statistic t used to test the hypothesis. Note that the population standard deviations are not known and therefore you cannot use the formula in Section 10.1. Use the one in Section 10.2 instead.
4. Compute the degree of freedom for the test statistic t.
5. Can the chain conclude that the mean waiting time for checkout at Store 1 is lower than that of Store 2? Use the critical-value approach and α = 0.05 to conduct the hypothesis test.
6. Construct a 95% confidence interval for the difference of mean waiting time for checkout line at the two stores.

PART B

1. Waiting time for checkout line at two stores of a supermarket chain were measured for a random sample of customers at each store. The chain wants to use this data to test the research (alternative) hypothesis that the mean waiting time for checkout at Store 1 is lower than that of Store 2. (12 points)

1. What are the null and alternative hypothesis for this research?
2. What are the sample mean waiting time for checkout line and the sample

standard deviation for the two stores?

3. Compute the test statistic t used to test the hypothesis. Note that the population standard deviations are not known and therefore you cannot use the formula in Section 10.1. Use the one in Section 10.2 instead.
4. Compute the degree of freedom for the test statistic t.
5. Can the chain conclude that the mean waiting time for checkout at Store 1 is lower than that of Store 2? Use the critical-value approach and α = 0.05 to conduct the hypothesis test.
6.    Construct a 95% confidence interval for the difference of mean waiting

time for checkout line at the two stores.

1. Waiting time for checkout line at two stores of a supermarket chain were measured for a random sample of customers at each store. The chain wants to use this data to test the research (alternative) hypothesis that the mean waiting time for checkout at Store 1 is lower than that of Store 2. (12 points)

1. What are the null and alternative hypothesis for this research?
2. What are the sample mean waiting time for checkout line and the sample standard deviation for the two stores?
3. Compute the test statistic t used to test the hypothesis. Note that the population standard deviations are not known and therefore you cannot use the formula in Section 10.1. Use the one in Section 10.2 instead.
4. Compute the degree of freedom for the test statistic t.
5. Can the chain conclude that the mean waiting time for checkout at Store 1 is lower than that of Store 2? Use the critical-value approach and α = 0.05 to conduct the hypothesis test.
6. Construct a 95% confidence interval for the difference of mean waiting time for checkout line at the two stores.
   

Sickle cell anemia is inherited as an autosomal, recessive disorder. Individuals who inherit the mutated gene from both parents will show symptoms of sickle cell, including a stiffening of the red blood cells when the individual is under conditions with low oxygen levels in the air (e.g. on top of a mountain). This can lead to low red blood cell count (anemia), shortness of breath, fatigue, jaundice, and joint pain. Most critically, the stiffened red blood cells can clog small blood vessels, blocking blood flow to critical organs (e.g. brain, lungs, liver, etc.) that can lead to death. Curiously, heterozygous carriers have a certain amount of resistance to malaria. The malaria parasite must invade red blood cells in order to develop and apparently the cell surface is altered in heterozygous individuals, thereby limiting the ability of the malaria parasite to enter the red blood cells. Recall that the rules for autosomal recessive diseases are that only the homozygous recessive individuals experience the symptoms of sickle cell anemia.

C.    Determine the results of a mating between two parents that are both heterozygous for sickle cell anemia.

1. Provide the Punnett square and the potential offspring phenotypes and genotypes.
2. What percentage of children from this mating will develop sickle cell anemia?
3. What percentage of children from this mating will carry at least one sickle cell allele?

(a) It is commonly accepted that there are gains from adding securities to an
investment portfolio. Explain what is meant by this statement. (Your answer
should include a discussion and example regarding systematic and
non‐systematic risk as well as an indication of the optimal number of assets to be
included within a portfolio in theory and in practice.)

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(b) The following table provides monthly percentage price changes for two well
known market indexes.

Month Russell
2000

Nikkei
1 0.04 0.04
2 0.10 ‐0.02
3 ‐0.04 0.07
4 0.03 0.02
5 0.11 0.02
6 ‐0.08 0.06

Answer the following:
(i) What have you assumed about the distribution of data (that is,
have you assumed the data is a sample or a population).

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(ii) Calculate the expected monthly rate of return and standard deviation for
each market index. (Hint: Use your calculator as no marks will be
provided for working in this particular question.)

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(iii) Calculate the correlation coefficient for Russell 2000 – Nikkei. (Hint: Use
your calculator as no marks will be provided for working in this particular
question.)