1.

Suppose a company called Hongyu F. Inc. is selling a product known as “Josue’s Giant Birthday Candles”. The company has the following table:

q           P             TR         TC         Profit         MR         MC         ∆Profit   

0           12                             4                               ---           ---               ---

1           11                             7                                                                  

2           10                                               8                                        

3             9                                                                                                  3                  

4             8                                                                               5                    

5             7                            29

What is the quantity produced?

a. 0

b. 2

c. 4

d. 5

2.

Again, suppose a company called Hongyu F. Inc. is selling a product known as “Josue’s Giant Birthday Candles”. As shown above, the company has the following table:

q           P             TR         TC         Profit         MR         MC         ∆Profit   

0           12                             4                               ---           ---               ---

1           11                           7                                                                  

2           10                                               8                                        

3             9                                                                                                  3                  

4             8                                                                               5                    

5             7                           29

Given this information from the previous problem, what is the relevant market structure?

a. Monopoly

b. Competitive

c. Slava-opoly

d. Raquel-opoly

3. Suppose a firm in the competitive market faces the following cost and revenue conditions: MC=$10; MR=$12. The firm should…

a. change nothing.

b. increase output.

c. increase price.

d. decrease output.

The marketing manager of a firm that produces laundry products decides to test market a new laundry product in each of the firm's two sales regions. He wants to determine whether there will be a difference in mean sales per market per month between the two regions. A random sample of 12 supermarkets from Region 1 had mean sales of 81.4 with a standard deviation of 8.4. A random sample of 17 supermarkets from Region 2 had a mean sales of 89.9 with a standard deviation of 6.4. Does the test marketing reveal a difference in potential mean sales per market in Region 2? Let μ1 be the mean sales per market in Region 1 and μ2μ2 be the mean sales per market in Region 2. Use a significance level of α=0.02 for the test. Assume that the population variances are not 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 of the t test statistic. Round your answer to three decimal places.

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

Step 4 of 4: State the test's conclusion.

The marketing manager of a firm that produces laundry products decides to test market a new laundry product in each of the firm's two sales regions. He wants to determine whether there will be a difference in mean sales per market per month between the two regions. A random sample of 13 supermarkets from Region 1 had mean sales of 72.7 with a standard deviation of 9. A random sample of 17 supermarkets from Region 2 had a mean sales of 84.9 with a standard deviation of 7.6. Does the test marketing reveal a difference in potential mean sales per market in Region 2? Let μ1 be the mean sales per market in Region 1 and μ2 be the mean sales per market in Region 2. Use a significance level of α=0.01 for the test. Assume that the population variances are not 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 of the t test statistic. Round your answer to three decimal places.

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

Step 4 of 4: State the test's conclusion.

The marketing manager of a firm that produces laundry products decides to test market a new laundry product in each of the firm's two sales regions. He wants to determine whether there will be a difference in mean sales per market per month between the two regions. A random sample of 12 supermarkets from Region 1 had mean sales of 84 with a standard deviation of 6.6. A random sample of 17 supermarkets from Region 2 had a mean sales of 78.3 with a standard deviation of 8.5. Does the test marketing reveal a difference in potential mean sales per market in Region 2? Let μ1 be the mean sales per market in Region 1 and μ2 be the mean sales per market in Region 2. Use a significance level of α=0.02 for the test. Assume that the population variances are not 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 of the t test statistic. Round your answer to three decimal places.
Step 3 of 4: Determine the decision rule for rejecting the null hypothesis H0. Round your answer to three decimal places.
Step 4 of 4: State the test's conclusion

Problem 4: Distinguishing between Point and Period Prevalence, Cumulative Incidence and Incidence Density at Happy Kids Day Care Center (11 points)

There were 11 children enrolled in the Happy Kids Day Care Center from the beginning of Month One until the end of Month Four. The 11 children were watched for a total of 4 months. The staff tries to keep good records about when children fall ill from disease X.

You are asked to inspect these records and report the following information. The information has been assembled in the figure above. The grey bar indicates the disease is present. For ease of calculations consider one month is equal to 30 days and disease begins on either the 1^st or 15^th of the month, except for Child #1 who was already ill when record-keeping began. Show all steps, including numerator and denominators. Express all final answers as percentages (multiplier of 100).         

1. Calculate the point prevalence of disease X at the end of Month 4. (2 points)
2. Calculate the period prevalence of disease X for the entire four months. (2 points)

The marketing manager of a firm that produces laundry products decides to test market a new laundry product in each of the firm's two sales regions. He wants to determine whether there will be a difference in mean sales per market per month between the two regions. A random sample of 12 12 supermarkets from Region 1 had mean sales of 77.7 with a standard deviation of 8.7. A random sample of 17 supermarkets from Region 2 had a mean sales of 82.5 with a standard deviation of 6.8. Does the test marketing reveal a difference in potential mean sales per market in Region 2? Let μ1 be the mean sales per market in Region 1 and μ2 be the mean sales per market in Region 2. Use a significance level of α=0.05 for the test. Assume that the population variances are not 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 of the t test statistic. Round your answer to three decimal places.

Step 3 of 4:

Determine the decision rule for rejecting the null hypothesis H0H0. Round your answer to three decimal places.

Step 4 of 4:

State the test's conclusion. (reject or fail to reject the null hypothesis)

Let V = R4 and let U = hu1, u2i, where u1 =    1 2 0 −3    , u2 =     1 −1 1 0    . 1. Determine dimU and dimV/U. 2. Let v1 =    1 0 0 −3    , v2 =     1 2 0 0    , v3 =     1 3 −1 −6    , v4 =     −2 2 0 9    . For any two of the vectors v1,...,v4, determine whether they are in the same coset of U in V or not. 3. Find a basis of V that contains a basis of U. Hence, determine a basis of V/U. 4. Find two (distinct) elements of the coset e1 + U.

A search for “car” on a shopping website gave a list of the following items:

You can use the following example problem as a model.

What are the “individuals” for this data set?

1-Kids

2-Customers

3-Items for sale on this website

4-Shopping website

Which of the following statements is NOT correct?

1-“Department” is a categorical variable

2-“Department” can be visualized using a bar plot

3-“Price” is a numerical variable

4-“Price” can be visualized using a pie chart

Explain how you reference in-text and in bibliography giving an example;
1 Journal article (2)
2 Internet source (2)
3 Book source (2)
4 Periodical (2)
5 Report (2)
6 Conference proceeding (2)
7 Newspaper article (2)

Starting with the Fourier transform pair

x ( t ) = u ( t + 1 )   -   u ( t - 1 )     ⇔   X ( Ω ) = 2 sin ( Ω ) / Ω

and using no integration indicate the properties of the Fourier transform that will allow you to compute the Fourier transform of the following signals

x 1 ( t )   =   - u ( t + 2 ) + 2 u ( t ) - u ( t - 2 )

x 2 ( t )   =   2 sin ( t )/ t

x 3 ( t )   =   2 [ u ( t + 0 . 5 ) - u ( t - 0 . 5 ) ]

x 4 ( t )   =   cos ( 0 . 5 πt ) [ u ( t + 1 ) - u ( t - 1 ) ].