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# HI6007 Statistics For Business Decision

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### Question 1

Below you are given the examination scores of 20 students

 52 99 92 86 84 63 72 76 95 88 92 58 65 79 80 90 75 74 56 99

a. Construct a frequency distribution, cumulative frequency distribution, relative frequency distribution, cumulative relative frequency distribution and percent frequency distribution for the data set using a class widthof

b. Construct a histogram showing the percent frequency distribution of the examination scores. Comment on the shape ofthe

### Question

Shown below is a portion of a computer output for a regression analysis relating supply (Y in thousands of units) and unit price (X in thousands of dollars).

 ANOVA df SS Regression 1 354.689 Residual 39 7035.262 Coefficients Standard Error Intercept 54.076 2.358 X 0.029 0.021

 a. What has been the sample size for this problem? b. Determine whether or not supply and unit price are related. Use α = 0.05. c. Compute the coefficient of determination and fully interpret its meaning. Be very specific. d. Compute the coefficient of correlation and explain the relationship between supply and unit price. e. Predict the supply (in units) when the unit price is \$50,000.

### Question 3

Allied Corporation wants to increase the productivity of its line workers. Four different programs have been suggested to help increase productivity. Twenty employees, making up a sample, have been randomly assigned to one of the four programs and their output for a day's work has been recorded. You are given the results below

 Program A Program B Program C Program D 150 150 185 175 130 120 220 150 120 135 190 120 180 160 180 130 145 110 175 175

 a. Construct an ANOVA table. b. As the statistical consultant to Allied, what would you advise them? Use a .05 level of significance.

### Question 4

A company has recorded data on the weekly sales for its product (y), the unit price of the competitor's product (x1), and advertising expenditures (x2). The data resulting from a random sample of 7 weeks follows. Use Excel's Regression Tool to answer the following

 Week Price Advertising Sales 1 .33 5 20 2 .25 2 14 3 .44 7 22 4 .40 9 21 5 .35 4 16 6 .39 8 19 7 .29 9 15 a. What is the estimated regression equation? Show the regression output. b. Determine whether the model is significant overall. Use α = 0.10. c. Determine if competitor’s price and advertising is individually significantly related to sales. Use α = 0.10. d.   e. Based on your answer to part (c), drop any insignificant independent variable(s) and re-estimate the model. What is the new estimated regression equation?    Interpret the slope coefficient(s) of the model from part (d).

a. Frequency descriptions

 Examination Score Frequency distribution Cumulative Frequency Relative Frequency Cumulative relative Frequency Percent Frequency 50-60 3 3 0.15 15% 15% 60-70 2 5 0.10 25% 10% 70-80 6 11 0.30 55% 30% 80-90 4 15 0.20 75% 20% 90-100 5 20 0.25 100% 25% Total 20

b. Construction of the histogram

The examination score between the range of 70-80 is responsible for 30% of the total scores. This means the range 70-80 is the modal class range.

1. Suppose the sample size is denoted by n and the number of regressions by k. by observing the regression output availed, k is given as 1. Being that

We can obtain , this gives us the value of n as 41

The sample size is therefore obtained as 41.

1. For x and y to be correlated, the coefficient of x must be a value other than zero.

For this reason, will test the hypothesis that the coefficient

Our hypothesis is therefore defined as

vs

The value of

The rejection rule is; reject the null hypothesis whenever the p value is less than the value of alpha.

Now we compute the p value

 SSR 354.689 SSE 7035.26 df Regression 1 df Error 39 F statistic 1.96622 p value 0.16876

The value is obtained as 0.16876, which is greater than alpha which is 0.05. we thereby fail to reject the null hypothesis.

We thereby conclude that there is sufficient evidence from the sample to prove that the coefficient of x is 0, this indicates that the values of x and y are not correlated.

1. The coefficient of determination will be obtained as 0 given that the two variables (x and y0 are independent of each other.
2. The coefficient of correlation is obtained as 0 given that the coefficient of determination is 0. This shows indecency among the two variables.
3. The output given can be used to derive the linear equation relating x and y as;

Fromm this equation we can substitute the value of x with 50000 and obtain the number of units as

1. Construction of the ANOVA table
 Anova: Single Factor SUMMARY Groups Count Sum Average Variance Program A 5 725 145 525 Program B 5 675 135 425 Program C 5 950 190 312.5 Program D 5 750 150 637.5 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 8750 3 2916.666667 6.140351 0.00557 3.238872 Within Groups 7600 16 475 Total 16350 19

1. Discussion and Recommendation

Suppose

The task needs the conduction of a hypothesis

vs at least one of the means is difference.

The

The p value is obtained from the excel output as 0.00557, compared to the value of

Alpha  this falls in the rejection region hence we reject the

Null hypothesis and conclude that the evidence indicates at least one of the means is

Difference.

The Advice to the Allied corporation is that there is a statistical difference among the

Outputs that arise from the workers under the difference. The firm therefore need to

specialise in the program that generates optimum output. This is specifically program

C.

1. Regression equation

Display of the multiple regression output

 SUMMARY OUTPUT Regression Statistics Multiple R 0.877814 R Square 0.770558 Adjusted R Square 0.655837 Standard Error 1.83741 Observations 7 ANOVA df SS MS F Significance F Regression 2 45.35284447 22.67642 6.716801 0.052644 Residual 4 13.50429839 3.376075 Total 6 58.85714286 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 90.0% Upper 90.0% Intercept 3.597615 4.052243833 0.887808 0.424805 -7.65322 14.84845 -5.04115 12.23638 Price 41.32002 13.33736254 3.098065 0.036289 4.289567 78.35048 12.88681 69.75324 Advertising 0.013242 0.327591655 0.040422 0.969694 -0.8963 0.922782 -0.68513 0.711617

The output can be used to derive the linear equation:

1. The significance of the model is given as 0.0526 which is less than the value of alpha (0.10). the conclusion is thus the model is statistically significant.
2. The competitors price p value is obtained from the model as 0.0362, this is lower than the alpha value hence the price can be stated to be statistically significant to the sales values.

Meanwhile the alpha value for advertising is given from the model as 0. l9697 which is higher than the value of alpha. Advertising is therefore not statistically significant to the sales value.

1. Revised regression model
 SUMMARY OUTPUT Regression Statistics Multiple R 0.877760967 R Square 0.770464315 Adjusted R Square 0.724557178 Standard Error 1.643764862 Observations 7 ANOVA df SS MS F Significance F Regression 1 45.34732824 45.34732824 16.7831053 0.009384894 Residual 5 13.50981461 2.701962923 Total 6 58.85714286 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 90.0% Upper 90.0% Intercept 3.581788441 3.608215389 0.992675895 0.366447177 -5.693424497 12.85700138 -3.688940109 10.85251699 Price 41.60305344 10.15521323 4.096718846 0.009384894 15.49824676 67.70786011 21.13980753 62.06629934

This model generates the linear equation;

1. The model has a slope of 41.60 which indicates that a unit increase in the price of the competitors goods raises the sales volume by 41.60 units.

## References

Andrew, G., 2008. Variance, analysis of. The new Palgrave dictionary of economics. 2nd ed. Basingstoke, Hampshire New York: Palgrave Macmillan.

Bailey, R. A., 2008. Design of Comparative Experiments, s.l.: Cambridge University Press.

Klaus, H. & & Oscar, K., 2008). . Design and Analysis of Experiments. I and II ed. s.l.:Wiley.

Scott, J. A., 2012. Illusions in Regression Analysis. International Journal of Forecasting, 28(3), p. 689.

Willem, W., Baets, D. & Luc, B., 2008. ROC analysis in ordinal regression learning. Pattern Recognition Letters, Volume 29, p. 1–9.

### Cite This Work

My Assignment Help (2019) Statistics For Business Decision [Online]. Available from: https://myassignmenthelp.com/free-samples/hi6007-statistics-for-business-decision
[Accessed 13 August 2020].

My Assignment Help. 'Statistics For Business Decision' (My Assignment Help, 2019) <https://myassignmenthelp.com/free-samples/hi6007-statistics-for-business-decision> accessed 13 August 2020.

My Assignment Help. Statistics For Business Decision [Internet]. My Assignment Help. 2019 [cited 13 August 2020]. Available from: https://myassignmenthelp.com/free-samples/hi6007-statistics-for-business-decision.

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