You are conducting a multinomial Goodness of Fit hypothesis test for the claim that the 4 categories occur with the following frequencies:

HoHo : pA=0.3pA=0.3;  pB=0.2pB=0.2;  pC=0.2pC=0.2;  pD=0.3pD=0.3

Complete the table. Report all answers accurate to two decimal places, unless otherwise specified.

What is the chi-square test-statistic for this data? (Round to two decimal places)
χ2=χ2=

What is the P-Value? (Round to four decimal places)
P-Value =


For significance level alpha 0.01,

What would be the conclusion of this hypothesis test?

• Fail to reject the Null Hypothesis
• Reject the Null Hypothesis

Report all answers accurate to three decimal places.

Kyle’s Shoe Stores Inc. is considering opening an additional suburban outlet. An aftertax expected cash flow of $160 per week is anticipated from two stores that are being evaluated. Both stores have positive net present values.

a. Compute the coefficient of variation for each site. (Do not round intermediate calculations. Round your answers to 3 decimal places.)

b. Which store site would you select based on the distribution of these cash flows? Use the coefficient of variation as your measure of risk.

• Site A

• Site B

You have estimated the following probability distributions of expected future returns for Stocks X and Y:

1. What is the expected rate of return for Stock X? Stock Y? Round your answers to one decimal place.
   Stock X:   %

   Stock Y:   %

2. What is the standard deviation of expected returns for Stock X? For Stock Y? Round your answers to two decimal places.
   Stock X:   %

   Stock Y:   %

3. Which stock would you consider to be riskier?   Stock X Or Stock Y?  is riskier because it has a -higher or lower? standard deviation of returns.

1. The following data shows the quarterly profit (in thousands of dollars) made by a particular company in the past 3 years.

a.  Use α = 0.3 to compute the exponential smoothing values for the time series. Compute MSE and the forecast of profit (in $1000s) for the next quarter.

b. Compare the three-period moving average forecast with the exponential smoothing forecast using α = 0.3. Which appears to provide the better forecast based on MSE?

Define the regression if the raw material used in production of a certain synthetic fiber measurement of the relative humidity the storage location and the moisture content.

Relative Humidity x 0.1×H+1 0.2×H+2 0.3×H+3 0.4×H+4 0.6×H+1 0.7×H+3 Moisture Content y 0.2×H×2 0.3×H×3 0.1×H+1 0.6×H+1 0.7×H+2 0.4×H+3 (a) Plot a graph Y vs. X showing these points or the graph is also called scatter diagram. (b) Calculate ∑ X, ∑ Y, ∑X2 , ∑Y2 , ∑XY, mean of X and mean of Y. (c) Calculate regression equation Y on X. (d) If ? = 82 find the estimated value of Y.

A random sample of 50 suspension helmets used by motorcycle riders and automobile race-car drivers was subjected to an impact test, and on 18 of these helmets some damage was observed.

(a)Test the hypotheses H0: p = 0.3 versus H1: p ≠ 0.3 with α = 0.05, using the normal approximation.

(b)Find the P-value for this test.

(c)Find a 95% two-sided confidence interval on the true proportion of helmets of this type that would show damage from this test. Explain how this confidence interval can be used to test the hypothesis in part (a).

(d)Using the point estimate of p obtained from the preliminary sample of 50 helmets, how many helmets must be tested to be 95% confident in order to keep the associated β-error at 0.1 (or the power at 90%)?

There are two routes to get from the student dorms to class - a long route, which is scenic, and a short route, which is not scenic. You want to study whether the route that the students choose to take is independent of the weather (in the context of the table, this will mean whether X and Y are independent), and you generate the accompanying table of probabilities.

Calculate E(X) and E(Y ).

(b) Calculate E(X | Y = 0). How is this different from E(X)?

(c) Are the route picked and the weather independent of each other? Why or why not? Use the numbers from the table to arrive at the answer.

A simple economy consists of two industries: agriculture and manufacturing. The production of 1 unit of agricultural products requires the consumption of 0.2 unit of agricultural products and 0.3 unit of manufactured goods. The production of 1 unit of manufactured goods requires the consumption of 0.4 unit of agricultural products and 0.3 unit of manufactured goods. (a) Find the total output of goods needed to satisfy a consumer demand for $100 million worth of agricultural products and $160 million worth of manufactured goods. (Round your answers to one decimal place.) agricultural products $ million manufactured goods $ million (b) Find the value of the goods consumed in the internal process of production in order to meet the gross output. (Round your answers to one decimal place.) agricultural products $ million manufactured goods $ million

3) The very first magnetic resonance imaging (MRI) devices employed multi-layer copper solenoids, like the one shown in the figure below. The solenoid dimensions were: length = 2 m and inner radius = 0.4 m. The required magnetic field was 0.3 T. Due to thermal considerations, the copper wire conductor was chosen to have a square cross-section, 10 mm×10 mm, which limited the maximum current in the conductor to 1,000 A.

A) What is the minimum number of solenoid layers needed to achieve the required magnetic field? Assume that the conductor in each layer is tightly wound on a cylinder, without any gaps.

B) For the chosen number of layers and using the copper resistivity value at room temperature, estimate the electrical power consumption of this solenoid at 0.3 T.

A professor has constructed a 3-by-4 two-dimensional array of float numbers. This array currently contains the lab grades, quiz grades and exam grades of three students in the professor’s class. Write a C++ program that calculate the final grade for each student and save it to the last column. You program should display the following output:             Lab    Quiz      Exam       Final    

Student 1          ## ## ## ##

Student 2          ## ## ## ##

Student 3          ## ## ## ##

The final grade consists of 30% lab grade, 30% quiz grade and 40% exam. For example, if lab grade is 95, quiz grade is 82 and exam grade is 87, the final grade is equal to 95∗0.3+82∗0.3+87∗0.4. Use random numbers between 40 and 100 for lab, quiz and exam grades.