Utility Problem Set

1. Suppose that the price of good X is $5 per unit and the price of good Y is $2 per unit. In addition, suppose that your income is $25

If you spend all your money on good X, how many units can you buy?

2. The table below shows total utility for two products. Suppose that the price for product X is $5 and the price for product B is $2.

Given this data, complete the table below:

Use the information above to answer questions 3 and 4:

The table below shows total utility for two products. Suppose that the price for product X is $5 and the price for product Y is $2.

3. Suppose that a person has $25.

How many units of each good should she buy to maximize her happiness given her budget constraint? Why?

4. Suppose income falls to $18. How many units of each good should she buy to maximize her happiness given her budget constraint? Why?

Can someone show me how to do a test for lack of fit for the following data?

Please show all work for an up vote. Thanks.

The quarterly sales of the TRK-50 mountain bike for the previous four years by a bicycle shop in Switzerland are presented in the table:

PLEASE USE EXCEL AND SHOW ALL WORK.

1. Plot the sales against time.
2. Use the data to estimate the monthly trend in sales using a linear trend model of the form:
   Q_t = a + bt. Does your statistical analysis indicate a trend? If so, is it an upward or downward trend and how great is it? Is it a statistically significant trend at 5 percent level of significance?
3. Now adjust your statistical model to account for seasonal variation in sales. Estimate this model of sales:
   Q_t = a + bt + cD₂ + dD₃ + eD₄
   where D₂, D₃, D₄ are the appropriately defined dummy variables for quarters 2, 3, and 4.
   Do the data indicate a statistically significant seasonal pattern at 5 percent level of significance? If so, what is the seasonal pattern of sales?
4. Comparing your estimates of the trend in sales in parts b and c, which estimate is likely to be more accurate? Why?
5. Using the estimated forecast equation from part c, forecast sales for Quarters 1 and 4 of 2014 and Quarters 2 and 3 of 2015.

Given the following sample information, test the hypothesis that the treatment means are equal at the 0.05 significance level. Treatment 1 - 8, 11 and 10. Treatment 2 - 3, 2, 1, 3, and 2. Treatment 3 - 3, 4, 5 and 4. - (a) Compute SST, SSE, and SS total. (Round your answers to 2 decimal places.) (b) Complete an ANOVA table. (Round your answers to 2 decimal places.) Source SS df MS F Treatments Error Total

An ammonia heat engine has the following reversible steps:

1 ? 2 Isothermal heating of saturated liquid @ 60°C to superheated vapor

2 ? 3 Adiabatic expansion to saturated vapor at -20°C

3 ? 4 Isothermal cooling to a 2 phase fluid

4 ? 1 Adiabatic compression back to state 1

Find QH (in kJ/kg). Use the correct sign convention to indicate the direction of heat. Hint: build a T-S diagram of the whole cycle first.

The atomic number of an element is 56. Which of the following statements are correct?
1. One atom of this element has 56 neutrons.
2. One atom of this element has 56 electrons.
3. One atom of this element has 56 protons.
4. One atom of this element has a total of 56 protons and electrons.
5. This element is bohrium.

Select one:

a. all five

b. 1, 4 and 5

c. 1, 2 and 3

d. 2 and 3

v

1. You are a financial analyst at Gen-Eric Corporation, and you are considering two mutually exclusive projects. Unfortunately, the figures for project 1 are in nominal terms and the figures for project 2 are in real terms. The nominal discount rate for both projects is 8%, and the inflation rate is projected to be 4%. Which project should you choose?

(4 pts)

A researcher compares two compounds (1 and 2) used in the manufacture of car tires that are designed to reduce braking distances for SUVs equipped with the tires. SUVs equipped with tires using compound 1 have a mean braking distance of 76 feet and a standard deviation of 8.9 feet. SUVs equipped with tires using compound 2 have a mean braking distance of 80 feet and a standard deviation of 14.6 feet. Suppose that a sample of 45 braking tests are performed for each compound. Using these results, test the claim that the braking distance for SUVs equipped with tires using compound 1 is shorter than the braking distance when compound 2 is used. Let μ1 be the true mean braking distance corresponding to compound 1 and μ2 be the true mean braking distance corresponding to compound 2. Use the 0.1 level of significance.

Step 1 of 4: State the null and alternative hypotheses for the test.

Step 2 of 4: Compute the value of the test statistic. Round your answer to two decimal places.

Step 3 of 4: Determine the decision rule for rejecting the null hypothesis H0. Round the numerical portion of your answer to two decimal places.

Step 4 of 4: Make the decision for the hypothesis test. Fail or reject to fail.

A study was designed to compare the attitudes of two groups of nursing students towards computers. Group 1 had previously taken a statistical methods course that involved significant computer interaction. Group 2 had taken a statistic methods course that did not use computers. The students' attitudes were measured by administering the Computer Anxiety Rating Scale (CARS). A random sample of 19 nursing students from Group 1 resulted in a mean score of 62.1 with a standard deviation of 4.4. A random sample of 12 nursing students from Group 2 resulted in a mean score of 71.3 with a standard deviation of 7.1. Can you conclude that the mean score for Group 1 is significantly lower than the mean score for Group 2? Let μ1 represent the mean score for Group 1 and μ2 represent the mean score for Group 2. Use a significance level of α=0.1 for the test. Assume that the population variances are equal and that the two populations are normally distributed. Step 1 of 4 : State the null and alternative hypotheses for the test. Step 2 of 4 :compute the value if the test statistic Step 3 of 4 : determine the decision rule for the null hypothesis, round to 3 decimal places. Step 4 of 4 Reject or fail hypothesis?

14. A researcher compares two compounds (1 and 2) used in the manufacture of car tires that are designed to reduce braking distances for SUVs equipped with the tires. SUVs equipped with tires using compound 1 have a mean braking distance of 44 feet and a standard deviation of 8.1 feet. SUVs equipped with tires using compound 2 have a mean braking distance of 47 feet and a standard deviation of 11.7 feet. Suppose that a sample of 51 braking tests are performed for each compound. Using these results, test the claim that the braking distance for SUVs equipped with tires using compound 1 is shorter than the braking distance when compound 2 is used. Let μ1 be the true mean braking distance corresponding to compound 1 and μ2 be the true mean braking distance corresponding to compound 2. Use the 0.05 level of significance.

Step 1 of 4: State the null and alternative hypotheses for the test.

Step 2 of 4: Compute the value of the test statistic. Round your answer to two decimal places.

Step 3 of 4: Determine the decision rule for rejecting the null hypothesis H0H0. Round the numerical portion of your answer to three decimal places.

Step 4 of 4: Make the decision for the hypothesis test.