1. Use the same data that was used in Assignment 1 which is the SWEETS-4-U2 data for the previous year which consists of 52 weekly values of the sales and costs for the two popular product lines namely *Forgive* and *Rejoice*.

These two products are both wrapped chocolates sold by weight. The only difference between *Forgive* and *Rejoice* is that different messages are attached to each type of chocolate. The *Forgive*chocolates have messages like “Sorry”, “Forgive Me” and “Trust Me” and the *Rejoice* chocolates have messages like “Celebrate”, “Have Fun” and “I Love You”.

The 52 Sales and Cost values for both types of chocolate are given in SWEETS-4-U2.xls.

The Accountant for SWEETS-4-U2 is worried that the business is spending too much on advertising for *Rejoice* as sales now exceed what the firm has budgeted for. In the business plan the firm had assumed that the average weekly sales for *Rejoice* was $450. If sales are more than $450 then the firm will be able to reduce its advertising spending.

(You can use Excel or your calculator for any calculations.)

[a] Using Excel and the weekly sales data find the mean and standard deviation of *Rejoice* Sales.

[b] Find the 90% interval estimate of the average weekly sales for *Rejoice*.

[c] Using a level of significance of a = 0.05 test whether the average of the weekly sales for *Rejoice*are more than 450.

[d] Briefly explain what a Type I error and what a Type II error are and what are their costs or consequences in this problem.

[e] Find the p value in this situation. Explain what the p value is and how we would use the p value to test the hypotheses.

[f] Using the p value test the hypotheses when the level of significance is a = 0.10

[g] Briefly explain how and when we can use an interval estimate when testing hypotheses.

2. Suppose the Sales manager of the Sweets-4-U2 chain of confectionary stores is interested in the relationship between Sales and Total costs for the *Rejoice* range of chocolates. i.e. how total cost is affected by sales, for the *Rejoice* product line.

The 52 Sales and Cost values for both types of chocolate are given in SWEETS-4-U2.xls.

Unless otherwise stated use a level of significance of a = 0.05.)

(You can use Excel or your calculator for any calculations.)

[a] Obtain the scatter diagram, the covariance and the correlation coefficient for Total Costs and Sales for the *Rejoice* chocolates. Briefly explain what this graph and these values are telling us about the relationship between Total Costs and Sales

[b] Write down the two forms of the Population Regression function you would assume here. Briefly explain how we interpret the conditional mean E(Y | X) and the error term (e).

[c] Estimate the sample regression function. Write down your estimated model and briefly explain what the estimated intercept and estimated slope are telling us about the relationship between the Total Costs and Sales for *Rejoice* chocolates.

[d] Using the F statistic, the R-squared value and the p-value for the estimated slope briefly discuss whether this estimated model does or does not show that there is a significant relationship between Total Costs and Sales for *Rejoice* chocolates.

(With a sample of n = 52 you can assume that the critical values for the t statistic are the same as the critical values for a z statistic.)

[e] Test the following hypotheses concerning the slope

H0 : b1 = 0.8 and H1 : b1 > 0.8

[f] Using you estimated model forecast the Total Costs when Sales are 200. Comment briefly on how useful this forecast will be.

Briefly explain what we mean by the terms “Prediction Interval” and “Confidence Interval”

[g] Using the F statistic, the R-squared value and the scatter diagram which shows the Residuals on the vertical axis and the values of Sales (our X variable) on the horizontal axis briefly discuss whether our estimated model can be seen as a reliable estimate of the relationship between Total Costs and Sales for *Rejoice* chocolates.

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