Hypothesis

1. Hypothesis testing:

The following is a test of whether intrinsic mean value is greater than extrinsic mean value, given that the sample size is n<30 then the T table is used to test this hypothesis, the following are the five steps used in testing the __hypothesis__.

a. Hypothesis:

Null hypothesis: H0: mean1 intrinsic = mean2 extrinsic

Alternative hypothesis: Ha: mean1 intrinsic ≠ mean2 extrinsic

Where mean1intrinsic is the mean intrinsic value and mean2 extrinsic is the mean extrinsic value

b. Test level:

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Hypothesis

This hypothesis is tested at the 95% level of test, however given that excel is used to determine the T statistics value then the critical value will also be determined.

c. T statistics:

When comparing two mean values from two samples then the formula used to determine the T statistics value is as follows:

T = (X1- X2)-(U1-U2)

─────────────

Square root [(S21/n1) + (S22/n2)]

Using the data analysis tool in Excel the t statistics values are determined, the tables below summarises the results for unequal and equal variances assumed:

Two-Sample (Equal Variances)

t-Test: Two-Sample Assuming Equal Variances

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Hypothesis

Variable 1

Variable 2

Mean

5.156

4.856

Variance

1.061733333

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**Hypothesis**

1.0559

Observations

25

25

Pooled Variance

1.058816667

Hypothesized Mean Difference

0

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Hypothesis

df

48

t Stat

1.030779747

P(T<=t) one-tail

0.153905095

t Critical one-tail

1.677224197

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Hypothesis

P(T<=t) two-tail

0.307810191

t Critical two-tail

2.010634722

Two-Sample (Unequal Variances)

t-Test: Two-Sample Assuming Unequal Variances

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Hypothesis

Variable 1

Variable 2

Mean

5.156

4.856

Variance

1.061733

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Hypothesis

1.0559

Observations

25

25

Hypothesized Mean Difference

0

df

48

t Stat

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__Hypothesis__

1.03078

P(T<=t) one-tail

0.153905

t Critical one-tail

1.677224

P(T<=t) two-tail

0.30781

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Hypothesis

t Critical two-tail

2.010635

d. T statistics and T critical value:

Equal variance:

When equal variance is assumed then:

T critical (two tail) =2.0106

T statistics = 1.03077

From the above T critical > T statistics, when this is the case the null hypothesis is accepted.

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Hypothesis

Results:

The null hypothesis H0: mean1 intrinsic = __mean2__ extrinsic when equal variances are assumed is accepted, this means that intrinsic and extrinsic mean values are equal:

Unequal variance:

T critical (two tail) =2.0106

T statistics = 1.03078

From the above T critical > T statistics, when this is the case the null hypothesis is accepted.

Results:

The null hypothesis H0: mean1 intrinsic = mean2 extrinsic when unequal variances are assumed is accepted, this means that intrinsic and extrinsic mean values are equal.

2. T __test__ and Z test:

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**Hypothesis**

The Z test is usually used when a researcher is comparing the *population* mean and the sample mean, in this case the population mean and standard deviation is known. The T test on the other hand is used to compare two sample mean values and therefore is used when the population mean and standard deviation is unknown. The Z test is used when the sample size is greater than 30 whereas the t test is used when the sample size is less than 30.

3. Sampling:

Data is collected from a sample instead of the population due to two reasons and this include cost and time, for example if the population size is 3 million then a study on the population will be more time consuming and costly than a study that will select a sample of 300 from the population.

REFERENCE:

Bluman, G. (2002). Elementary statistics. New York: McGraw Hill publishers

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