Type and Price of Products

Introduction:

This paper tends to find out whether the price for one type of a product is more expensive than the other; in this case data is selected including the type of product, the price and the age. However the only relevant data is the data regarding the price and the type, the type is assigned numerical values 0 and 1 and therefore we have two types of the product, prices range from 10,000 to 4000 and using the sample means we will be in a position to formulate our hypothesis which we will test.

Data:

The sample whose n = 80 contains both types, the table below summarizes some of the central tendencies of the entire sample data:

Price

Price(\$000)

Age

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Type and Price of Products

Type

total

1857453

1857.453

3372

50

mean

23218.1625

23.21816

42.15

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Type and Price of Products

median

22831

22.831

42.5

mode

20642

20.642

46

1

standard deviation

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Type and Price of Products

4354.43781

4.354438

8.217148

From the table the mean price is 23218.1625 while the mean age is 42.15, the standard deviation for the price is 4354.43 meaning that the data deviates 4354.43 from the mean, the mode for the type data is 1 and from the total it means that type 1 has 50 units of data while type 0 has 30 units of data, the mean value oif price gives us the average price of products in this sample, we now check the mean value for both types.

type 0

type 1

n

30

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Type and Price of Products

50

total

775386

1082067

mean

25846.2

21641.34

median

24414.5

20642

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Type and Price of Products

mode

#N/A

20642

standard deviation

4288.838

3594.166144

From the table that summarizes values for both types it is evident that type 0 has a greater mean than type 1, type 0 has a mean value of 25846 while type 0 has a mean value of 21641, however type 0 has a higher standard deviation value than type 1, we now investigate whether type 0 is more costly than type 1.

Hypothesis:

From our above analysis of our sample data type 0 has a higher mean price than type 1, we tend to investigate through hypothesis testing whether type 0 is more expensive than type 1, we state our hypothesis as follows:

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Type and Price of Products

The mean price for type 0 is greater than the mean price for type 1

We now state our null and alternative hypothesis as follows:

We assume that the mean price for type 0 is a1 while the mean price for type 1 to be a2, we state the null hypothesis as follows:

Null hypothesis:

H0: a1 = a2

Alternative hypothesis:

H0: a1 >a2

Having stated our null hypothesis as a1 = a2 this means that both means are equal and non of the types is more costly than the other type, it can also be stated as a1 – a2 = 0 because the alternative hypothesis means that the mean price for type 0 is greater than the mean price for type 1.

Test statistics:

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Type and Price of Products

To test the difference between two mean we use the following formula to determine the calculated value;

A1–A2

T Calculated  =  ___________

((σ12/ n1) + (σ22/ n2)) ½

Where σ1is the standard deviation for type 0 while σ2 is the standard deviation for type 1

In our case we will substitute our values as follows:

type 0

type 1

n

30

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Type and Price of Products

50

total

775386

1082067

mean

25846.2

21641.34

median

24414.5

20642

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Type and Price of Products

mode

#N/A

20642

standard deviation

4288.838

3594.166144

variance

18394131

12918030.27

25846.2 – 21641.34

T calculated  =  ______________________

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Type and Price of Products

((18394131/ 30) + (12918030.27/ 50)) ½

4204.86

T calculated  =  ______________________

((613137.7) + (258360.6054)) ½

4204.86

T calculated  =  ______________________

(871498.2914) ½

T calculated  = 4204.86/ 933.5407

T calculated  = 4.504206

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Type and Price of Products

After determining our T calculated is determined we now determine the level of test, we base our test on the 98% level of test using the table, a two tail 98% level of test from the table the critical value is 2.374.

The T calculated > T critical, this can be demonstrated in the diagram below:

Because the T calculated > T critical then we reject the null hypothesis that a1 = a2, by rejcting the null hypothesis it means that we accept the alternative hypothesis which is a1 >a2, this therefore means that type 0 products are more expensive than type 1 products, this means that at 98% level of test we have tested our hypothesis that type 0 is more expensive than type 1 products,

Having tested our hypothesis we can now rely on the results to make decisions, it is evident that type 0 products are more expensive than type 1 products, in order for proper decision making it is important to choose the type 1 product which is less expensive and also the producers of this product may decide to lower prices in order for them to increase the demand for their product, by reducing the price the demand would rise for type 0 and this would mean increased profit levels. Consumers will also benefit in the process in that lower prices would mean an increase in consumer surplus and also real income.

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Type and Price of Products

References:

Burbidge S. (1993) Statistics: An Introduction to Quantitative Research, McGraw Hill, New York

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