Report:

Extrinsic and intrinsic are two variables in the AIU data set that are measures of satisfaction, and one variable(intrinsic) indicates employee satisfaction in their day to day job activities while the other variable(extrinsic) indicates external factors satisfaction. The mean values are 5.116 and 4.736 for intrinsic and extrinsic respectively. This is an indication that the intrinsic mean is greater than the extrinsic mean, in order to check whether the two means are different a T test is undertaken to check whether there is a significant difference in the mean values at the 0.05 level of significance.

Hypothesis:

H0: M1 = M2

H1: M1>M2

Where M1 is the intrinsic mean and M2 is the extrinsic mean.

Level of test:

Given that the alternative hypothesis states that M1>M2 therefore a one tail T test is undertaken, the *level* of test is 0.05.

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Results:

The following are the results:

t-Test: Two-Sample Assuming Unequal Variances

INTRINSIC

EXTRINSIC

Mean

5.116

4.736

Variance

1.068066667

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1.1224

Observations

25

25

Hypothesized Mean **Difference**

0

df

48

t Stat

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1.283764248

P(T<=t) one-tail

0.102693583

t Critical one-tail

1.677224197

P(T<=t) two-tail

0.205387165

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t Critical two-tail

2.010634722

Decision:

The T statistics value is 1.283764248, the T critical value (one tail) is 1.677224197, and the decision is as follows:

The T statistics value is 1.28 while the T critical value is 1.667, given that the critical value is greater then the hypothesis H0: M 1 = M2 is accepted. (McClave, 2008)

Implication:

Hypothesis H0: M1 = M2 is accepted meaning that extrinsic and intrinsic mean values are equal, and therefore there exist no significant difference between the two means at the 0.05 level of significance. The conclusion is that despite the two means value being different, at the 0.05 level of significance the two means are equal, this shows that the intrinsic and extrinsic mean value are equal.

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Z tests and T tests:

When testing for the difference between two mean value then either a Z test or a T test is used, A T test is used *when* the population means value is unknown whereas a z test is used when the population mean value is know, for example given that the population mean is 546 and a sample obtained from the same population is 490, a test to check whether these values are different then a Z test is undertaken. The other reason is the size of the sample, a sample size that is greater than 30 units a Z test is undertaken and a T test is used if the sample size is less than 30 units. (McClave, 2008)

Samples:

Kalton (1993) describes a number of reasons why samples are sued, according to him an example of a study that is undertaken on the population is a country’s *census*, this is a very expensive exercise and therefore a sample is used instead of a population to reduce costs. The other reason is that a study on a population is time consuming and therefore a sample is selected in order to speed up the data collection process, another reason why a sample is used is because more information can be collected from a sample with limited resources and time than a population. (Kalton, 1993)

References:

Graham Kalton (1993) Introduction to survey sampling, NY: Blackwell publishers

James McClave (2008) Statistics for business and economics, NJ: Prentice Hall publishers

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