Hypothesis Test

Two sample means hypothesis test:

The following is a test to determine whether extrinsic mean is equal to intrinsic mean value:

a. Null hypothesis:

H0: X1 = X2  b. Alternative hypothesis: H1: X1 ≠X2

Where X1 is extrinsic mean value and X2 is intrinsic mean value:

The table below copied from Excel summarises the results:

t-Test: Two-Sample Assuming Unequal  Variances

Hypothesis Test

EXTRINSIC

INTRINSIC

Mean

4.856

5.156

Variance

1.0559

1.061733333

Observations

25

Hypothesis Test

25

Hypothesized Mean Difference

0

df

48

t Stat

-1.030779747

Hypothesis Test

P(T<=t) one-tail

0.153905095

t Critical one-tail

1.677224197

P(T<=t) two-tail

0.307810191

t Critical two-tail

2.010634722

Hypothesis Test

The T statistics value is -1.0307797

The two tail critical value is 2.0106347

Decision:

The diagram shows the rejection region of the null hypothesis:

Given that -1.03 is in the acceptance region the null hypothesis H0: X1 = X2 is accepted; therefore the two means are equal at the 0.05 level of confidence.

Population versus sample:

There are various methods used in determining a sample and they are categorised into probability and non probability sampling methods, a sample is usually selected due to various reasons and this include the available resources to undertake a study, resources mean time and funds required to undertake the study whereby a sample is considered to save both time and money given that data is collected from only a few respondents.

Z and T tests:

Hypothesis Test

Statistical methods involve using both the T table and the normal distribution; a t test will use the T distribution table while a z test will use the normal distribution table when determining critical values. A t test is used when the sample size n<30 and will be used when comparing sample means, a Z test is used when the sample size n>30 and will be used to compare sample and population mean values.

## References:

Douglas Lind (1998). Statistics: An Introduction. London: Macmillan

January, from < http://www.stattutorials.com/EXCEL/EXCEL_TTEST2.html >