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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).

a) Prepare a frequency distribution, relative frequency distribution, and percent frequency distribution for the data set using a class width of $50.

Furniture order Value in $	Frequency	Relative frequency	Percentage frequency
120-170	8	0.16	16
171-220	15	0.3	30
221-270	12	0.24	24
271-320	4	0.08	8
321-370	5	0.1	10
371-420	2	0.04	4
421-470	2	0.04	4
471-520	2	0.04	4
	50	1	100

 

b) Construct a histogram showing the percent frequency distribution of the furniture-order values in the sample. Comment on the shape of the distribution.

The histogram of furniture order value shows that the maximum percentage of order is in the range of class 171-220 which is 30% of the overall volume.

c) Given the shape of the distribution in part b, what measure of location would be most appropriate for this data set?

The most appropriate location for the given data set is 171-220 class with overall sale of 30%.

Question 2

Shown below is a portion of a computer output for a regression analysis relating Y (demand) and X (unit price).

a) Determine whether or not demand and unit price are related. Use α = 0.05

Obtained F ratio = 74.13685298

F critical (1, 46) = 3.79E-11, at 0.05 significance level

My obtained F-ratio is larger than this, and so I conclude that my obtained F-ratio is likely to occur by chance with a p<.05

b) Compute the coefficient of determination and fully interpret its meaning.

Coefficient of determination is R^2 value. It tells us percentage variation in Y explained by the regression analysis.

Our R¬^2 = SS reg/SS total = 0.617103338

So there is 61.71 % variation explained

c) Compute the coefficient of correlation and explain the relationship between demand and unit price.

Coefficient of determination is R^2 value 0.785559252

Since X is negative therefore R value is also negative which signifies a negative relationship between X and Y.

Question 3

The following are the results from a completely randomized design consisting of 3 treatments.

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.

I = no. of treatment so, degree of freedom for treatment is 3-1 = 2

So, Residual = 21

Total no. of observation = 24

Obtained F ratio = 25.8907197

F critical (2, 21) = 2.14826E-06, at 0.05 significance level

My obtained F-ratio is larger than this, and so I conclude that my obtained F-ratio is likely to occur by chance with a p<.05. There is difference between the different groups.

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.

a) Develop an estimated regression equation relating y to x₁ and x₂.

Estimated regression equation relating y to x1 and x2.

Y =b­₀+ b­₁X₁ + b­₂X₂

=0.8051+ 0.4977(price) + 0.4733 (no. of advertising spot)

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.

No. of degree of freedom = nk-1

= 7*3-1

=20

	df	SS	MS	f
Regression	2	40.7	20.35	360.5314961
Residual	18	1.016	0.056444444
Total	20	41.716

F critical (2, 18) = 3.01522E-15 , at 0.05 significance level

My obtained F-ratio is larger than this, and so I conclude that my obtained F-ratio is likely to occur by chance with a p<.05.

c) At α = 0.05, test to see if β1 and β2 is significantly different from zero.

H0 : β1 = 0

H0 : β1 = β2= is not 0

β1 and β2 is significantly different from zero

d) Interpret slope coefficient for X₂.

Slope of X2 = R* Sy/Sx

Slope = 0.98*18.98

          = 18.75

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?

Mobile phones = 0.8051+ 0.4977(price) + 0.4733 (no. of advertising spot)

                        =0.8051+ 0.4977*20000+ 0.4733 *10

                                =9959.538

                        = 9960 Aprox…

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