Question 1 - Missy Walters owns a mail-order business specializing in clothing, linens, and furniture for children. She is considering offering her customers a discount on shipping charges for furniture based on the dollar-amount of the furniture order. Before Missy decides the discount policy, she needs a better understanding of the dollar-amount distribution of the furniture orders she receives.
Missy had an assistant randomly select 50 recent orders that included furniture. The assistant recorded the value, to the nearest dollar, of the furniture portion of each order. The data collected is listed below (data set also provided in accompanying MS Excel file).
136 281 226 123 178 445 231 389 196 175
211 162 212 241 182 290 434 167 246 338
194 242 368 258 323 196 183 209 198 212
277 348 173 409 264 237 490 222 472 248
231 154 166 214 311 141 159 362 189 260
a. Prepare a frequency distribution, relative frequency distribution, and percent frequency distribution for the data set using a class width of $50.
b. Construct a histogram showing the percent frequency distribution of the furniture-order values in the sample. Comment on the shape of the distribution.
c. Given the shape of the distribution in part b, what measure of location would be most appropriate for this data set?
Question 2 - Shown below is a portion of a computer output for a regression analysis relating Y (demand) and X (unit price).
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ANOVA
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|
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df
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SS
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Regression
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1
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5048.818
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Residual
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46
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3132.661
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Total
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47
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8181.479
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|
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Coefficients
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Standard Error
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Intercept
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80.390
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3.102
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X
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-2.137
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0.248
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a. Determine whether or not demand and unit price are related. Use α = 0.05.
b. Compute the coefficient of determination and fully interpret its meaning. Be very specific.
c. Compute the coefficient of correlation and explain the relationship between demand and unit price.
Question 3 - The following are the results from a completely randomized design consisting of 3 treatments.
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Source of Variation
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Sum of Squares
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Degree of Freedom
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Mean Square
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F
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Between Treatments
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390.58
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|
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|
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Within Treatments (Error)
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158.40
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|
|
|
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Total
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548.98
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23
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|
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Using α = .05, test to see if there is a significant difference among the means of the three populations. The sample sizes for the three treatments are equal.
Question 4 - In order to determine whether or not the number of mobile phones sold per day (y) is related to price (x1 in $1,000), and the number of advertising spots (x2), data were gathered for 7 days. Part of the Excel output is shown below.
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ANOVA
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|
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df
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SS
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MS
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F
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Regression
|
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40.700
|
|
|
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Residual
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1.016
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|
|
|
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Coefficients
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Standard Error
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Intercept
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0.8051
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|
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x1
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0.4977
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0.4617
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x2
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0.4733
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0.0387
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a. Develop an estimated regression equation relating y to x1 and x2.
b. At α = 0.05, test to determine if the estimated equation developed in Part a represents a significant relationship between all the independent variables and the dependent variable.
c. At α = 0.05, test to see if β1 and β2 is significantly different from zero.
d. Interpret slope coefficient for X2.
e. If the company charges $20,000 for each phone and uses 10 advertising spots, how many mobile phones would you expect them to sell in a day?
Question 5 - A clinic offers a weight reduction program. A review of its records found the following weight losses, in pounds, for a random sample of ten of its patients at the conclusion of the program.
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18.2
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25.9
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6.3
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11.8
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15.4
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20.3
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16.8
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19.5
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12.3
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17.2
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Assume the population distribution is normal. Use Excel to compute necessary statistics and probabilities.
(a) Find a 99% confidence interval for the population mean weight-loss.
(b) Using the result in (a), test at the 1% significance level the null hypothesis that the population mean equals 20 against the two-sided alternative.
(c) Test the null hypothesis that the population mean weight-loss equals 20 pounds against the one-sided alternative hypothesis that the population mean weight-loss is lower than 20 pounds at the 5% level.
(d) Find the p-value of the above test in (c).
(e) Suppose that the population mean is in fact 20. What is the probability that the null hypothesis will be rejected (Type I error) in (a)?
(f) Suppose the population mean is in fact 19 and the population standard deviation is 5. What is the probability that the test
H0: μ = 20,
H1: μ < 20
will not reject the null against the alternative at the 5% level (Type II error)?
Question 6 - Samples of size 12 were drawn independently from two normal populations. A matched pairs experiment was then conducted from the same populations. These data are stored in Excel file named "Two_samples.xls".
a) Using Excel, calculate the descriptive statistics of the two independent samples.
b) Using the data taken from independent samples, test by hand to determine whether the variances of the two populations differ at the 5% significance level. Use Excel to confirm your test results and attach your Excel output table.
c) Using the data taken from independent samples, test by hand to determine whether the means of the two populations differ (assume equal variance) at the 5% significance level. Use Excel to confirm your test results and attach your Excel output table.
d) Repeat part (c), using the matched pairs data.
e) Is the required condition for the test in part (c) and (d) satisfied? Why?
f) Describe the differences between part (c) and (d). Discuss why these differences occurred.
Question7 - Stock prices and interest rates are key economic indicators. Investors in stock markets, individual or institutional, watch very carefully the movements in the interest rate. As a measure of stock prices, let us use the S&P 500 composite index, and as a measure of the interest rate, let us use the three-month Treasury bill rate. The data on these variables are provided in Stock.xlsx for the period 1980-2007.
a) What relationship, if any, do you expect between interest rates and stock prices? Why?
b) Plot using Eviews or Excel the scattergram between interest rates (x-axis) and stock prices (y-axis). Does the scattergram support your expectation in part (a)?
c) Let Yt be the S&P500 index and Xt be the three-month Treasury bill rate. Using Eviews or Excel, estimate the following regression Yt = β1 + β2Xt + εt.
Provide the Eviews or Excel output and write down the fitted equation (include the predictive equation, t-statistics of the estimated model parameters, and sample size).
d) Interpret the coefficients. Does the sign of the slope coefficient consistent with your expectation?
e) Test by hand the significance of the slope coefficient at the 5% significant level.
Question 8 - Suppose the regression model is
Yt = β1 + β2Xt + εt.
The OLS estimator of the slope coefficient is
Β^1 = ∑(Xi - X-)(Yi - Y-)/∑(Xi - X-)2
Show that the OLS slope estimator is a linear functions of Yi.
Note - MS Excel must be used for performing calculation/graphical presentation as required in this assignment.
Attachment:- Data set - Question 1.rar