HI6007 Statistics For Business Decisions

Questions:

1 .

Below you are given the examination scores of 20 students  

2.

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).

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  

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

1.

a. Frequency table

b. Histogram

The histogram above clearly refers to the presence of positive skew due to which the shape of the graph is asymmetric. This can be inferred from a right side tail which is present. Hence, it ca also be concluded that the above distribution cannot be termed as normal distribution.

1. Mean as an indicator of central tendency is used when the shape of the graph is symmetric which implies that outliers are not present in the data. However, this is not the case here and median would be a better choice considering that it is immune to distortion from extreme values.

1. ‘Demand and unit price are related’

• Hypotheses

• Significant relation does exist between unit price and demand. 

(b) The value of coefficient of determination

Correlation of determination

The sign of coefficient of correlation would depend on the sign of independent variable slope coefficient. Therefore, the negative sign of slope coefficient (unit price) implies that the coefficient of correlation is negative (). price. This refers to the lower price beig conducive to higher demand.

3.

• Hypotheses

4.

• Since, (0.00<0.05), thus reject null hypothesis
• “Significant relationship is present between at least one of the independent variables and dependent variable.”

1. Hypothesis testing for slope coefficients

(d) The x2 slope coefficient is indicative of the fact that the change in the mobile phone advertising spots tends to bring about a change in the daily sales of mobile phone by 0.4733 units. The direction of change for these two variables is the same owing to positive value of the slope coefficient.

(e)  Number of mobile set sold for mobile unit price of $20,000 and 10 advertising spots.

Therefore, 9960 is the total number of mobile sets sold for mobile unit price of $20,000 and 10 advertising spots.