Minutes To Drive To Work

The following is an analysis of whether there are changes occurring to the time taken to drive to work, the table below summarizes the mean and standard deviation of the two samples:

current

previous

1

20

30

2

20

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Minutes To Drive To Work

30

3

30

20

4

30

20

5

30

total

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Minutes To Drive To Work

130

100

average

26

25

standard  deviation

5.477225575

5.773503

The above case ignores the time taken to drive to work for the periods when the individual did not report to work. Current mean value is 26 minutes and previous mean was 25 minutes and this shows that there has been an increase in the average time taken to drive to work.

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Minutes To Drive To Work

Hypothesis:

In order to determine whether there is a difference in mean time taken to drive to work a hypothesis is stated that will be tested using the T distribution.

Null hypothesis:

H0: C=P

Alternative:

Ha: C>P

Where C is the current mean time taken to drive to work and P is the previous mean time taken to drive to work.

Level of test:

The 95% test level using the T distribution is selected. One of the assumptions is that the data assumes a normal distribution.

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Test statistics:

Given that two means are being compared with unequal variance the following formula is used:

T = [(C-P)/ {(σc2/nc) + (σp2/np)} ½]

Where σc and σp is current data standard deviation and previous data standard deviation

respectively, n c and np is current data sample size and previous data sample size respectively.

The values are substituted as follows:

T = [(26-25)/ {(5.4772255752/5) + (5.7735032/4)} ½]

T statistics = 0.264135272

Critical value:

At the 95% two tail tests, degree of freedom = 5- 1 = 4, the critical value is 2.7764.

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Decision:

T statistics < T critical

Given the above results the null hypothesis H0: C=P is accepted, this hypothesis states that the two means are equal, for this reason the two means are equal.

Interpretation:

From the hypothesis test the means for the two samples are equal and this means that the current data mean time taken to drive to work is equal to the previous data mean time taken to drive to work at the 95% test level. The mean time taken to drive to work is constant according to the hypothesis test, however a larger sample size will provide more accurate results.

## REFERENCE:

Mendenhall, W. (2003) Introduction to statistics, Prentice Hall press, New  Jersey

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Minutes To Drive To Work