Hypothesis Testing

I. Hypothesis Testing

A. given

Dual Degree MBA Students

Regular MBA Students

n1 = 100

n2 = 100

μ1 = 84

μ2 = 87

σ1 = 4.0

σ2 = 5.0

α1 = 0.1

 α­2 = 0.1

 

The solution:

1. Ho : μ1 = μ2

2. H1 : μ1 < μ2

3.  α = 0.1

4. Critical region: z < -1. 28

Reject Ho if z > -1.28

 

 

Where z =       (n1 – n2)

                 √ (σ12 / n1 + σ22/ n2)

                =       (84- 87)

                 √ (16 / 100+ 25/100)

              z = -3/0.64

              z ≈ -3.75

5. Since the value of z < -1.28.

Then accept Ho that there is no difference between the dual degree and the regular MBA Students in terms of scores.

 

 

II. Regression Analysis

a. The scatter diagram for the data is given below:

To get the correlation or relationship of the advertising cost ($) and the number of orders, it is important to use the formula for Pearson r correlation which is:

                            

Using the formula above, the value of r is 0.857 which means that two variables, the price of advertisement and the number of orders are highly correlated or has the strong relationship.

 

b. Using the least square method, the regression equation can determine:

The regression equation will be y = 819,880.05 + 50,526.45x. This means that the advertising cost can be manipulated by substituting the value of the number of orders in y variable so that it can manipulate the value of x which is the price of advertisement.

 

c. For the definition of the slope in the regression which is 50,526.45. This means that for every of the advertising cost, it is expected that the increase in orders will be 50,526.45 order or approximately 50,526 orders.

 

d. To get the monthly advertising cost with an orders of 4,999,000 and with the aide of the regression equation. The value of the advertising cost will be:

y = 819,880.05 + 50,526.45x

4,999,000 = 819,880.05 + 50,526.45x

4,999,000 – 819,880.05 = 50,526.45x

4,179,119.95 = 50,526.45x

  50,526.45        50,526.45

x =.71

 

e. For this problem, coefficient of variation or r2 is equal to 0.735 or 73.55% of the total variation in number of orders can be explained by the price of the advertisement.

f. Standard error of estimate for the given problem is

The formula yield for the value of standard error of estimate which is 6.23 it is the error in estimating for the value of prices of advertisement. This also means that the value smaller the value of Sest  is also the more accurate the predictions.

 

 

 

Credit:ivythesis.typepad.com