HI6007 Statics For Business Decisions

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25-11-2020

Course Code: HI6007
University: Holmes Institute

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Country: Australia

Question:

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 furnitureorder 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?

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

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.
Source of Variation
Sum of
Squares
Degrees of
Freedom
Mean
Square F
Between Treatments 390.58
Within Treatments (Error) 158.40
Total 548.98 23
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 .Coefficients Standard Error
Intercept 0.8051
x1 0.4977 0.4617
x2 0.4733 0.0387

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?

Answer:

The required frequency distribution, relative frequency distribution, and percent frequency distribution is calculated in Excel, the calculated values is,

The maximum number of peaks goes to the left side and a log tail to the right side, so data in sample is positively skewed.

As, the data is positively skewed so the outliers belongs to the dataset. Thus, in this case the middle vale of the data (Median) will be the most appropriate measure of the center location.

Answer 2

The null hypothesis for the test is slope is 0 and the alternate hypothesis is slope is different from 0. The t- test will be used to determine whether demand and unit price are related.The calculations are done in excel, the value of the t-test statistic is, -8.61 and the corresponding P-value at 46 degree of freedom and two tailed test is 0.000.

The, P-Value is less than the significance level, so the null hypothesis gets rejected. Hence, it can be conclude that, demand and unit price are related.

The formula to calculate the coefficient of determination is R-Square =(SSR/SST). The calculations are done in excel. The value of R-Square is 0.6171. So, 61.71% of the variation in demand explained by the unit price in the regression equation.

The calculation are done in excel, the value of the correlation coefficient between demand and unit price is 0.7856. Thus, the value of correlation coefficient is near to 1, so it can say that there is a strong positive relationship between demand and the unit price, as the unit price increases demand also increases.

Answer 3

The formulas of the completely randomized design is,

Source of variation	Sum of squares	Degrees of freedom	Mean square	F-Statistic
Between Treatments	SSTR	k-1	SSTR/k-1	(SSTR/k-1)/(SSE/n-k)
Within Treatments	SSE	n-k	SSE/n-k
Total	SST	n-1

The calculations are done in excel, the calculated values are shown below,

Source of variation	Sum of squares	Degrees of freedom	Mean square	F-Statistic
Between Treatments	390.58	2	195.29	25.89
Within Treatments	158.4	21	7.54
Total	548.98	23

The, P-Value is 0.000. So, the P-value is less than the 5% level of significance. Thus, the null hypothesis of the test gets rejected. Hence, there is statistically significance difference among the means of the three populations.

Answer 4

The estimated regression equation relating Y to X₁ and X₂ is

Y= 0.8051+0.4977 (X₁) + 0.4733 (X₂)

The null hypothesis for the F-test is, all the slope coefficient is 0. And the alternate hypothesis is, at least one of the slope coefficient is different from 0.

The calculations are done in excel, the value of test statistic is 80.12 and the corresponding P-Value is 0.000. The P-Value is less than the 5% level of significance, so the null hypothesis of the test gets rejected. Hence, there is statistically sufficient evidence to conclude that, there is a significant relationship between all independent variables and dependent variables.

The null hypothesis for the test is slope for X₁ is 0 and the alternate hypothesis is slope is different from 0.The calculations are done in excel, the value of the t-test statistic is, 1.078 and the corresponding P-value at 4 degree of freedom and two tailed test is 0.3417.

The, P-Value is greater than the significance level, so the null hypothesis does not gets rejected. Hence, it can be conclude that, slope of X₁ is not different from 0.The null hypothesis for the test is slope for X₂ is 0 and the alternate hypothesis is slope is different from 0.The calculations are done in excel, the value of the t-test statistic is, 12.23 and the corresponding P-value at 4 degree of freedom and two tailed test is 0.0003.

The, P-Value is less than the significance level, so the null hypothesis gets rejected. Hence, it can be conclude that, slope of X₁ is different from 0.The estimated slope for advertising sports is 0.4733, the slope indicates that as the advertising sports increases by 1 the mobile phone sold per day will increases by 0.4733 percentages.