# Chi Square Test for the Data

2021-04-27
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Typically, blood pressure implies to the arterial pressure exerted during the systemic circulation of blood in the body. The blood pressure is medically perceived as the stress exerted by blood circulating in the body upon the blood vessels. Blood pressure (BP) is universally expressed as maximum pressure (Systolic) over the minimum pressure (Diastolic). The normal blood pressure that an adult at rest should have is 120/80 mm Hg.

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The blood pressure varies depending on various situation that a person is. Different activities yield different blood pressure levels and so does different disease or emotional states. Our data at hand shows the blood pressure for a 29 individuals doing different kind of jobs. Does the type of job influence the blood pressure level? Is there a significant difference in blood pressure across the different type of jobs? These are some of the questions that a researcher would be interested in answering.

Using a chi square test, we determine whether the blood pressure, systolic and diastolic, are significantly different and independent of job type. The acceptable range of diastolic pressure is 60-79 while the acceptable limit of systolic is 110-139. Any value beyond these ranges is considered abnormal.

The resulting contingency table is:

 Normal range Abnormal range Row Total Systolic 24 5 29 Diastolic 12 17 29 Total 36 22

The resulting calculated expected table of values from the formulae: E = row total. Expected number in brackets.

 Normal range Abnormal range Total Systolic 24 (18) 5 (11) 29 Diastolic 12 (18) 17 (11) 29 Total 29 29 58

The calculated Chi Square statistic is calculated as:

x2=O-E2Ex2=24-18218+5-11211+12-18218+17-11211=10.5454 the hypothesis to be tested:

H0: There is independence of data

H1: There is no independence of datathe 5% level of significance x value from x2 tables is 3.841

Conclusion

The computed x2=10.5454, is greater than the tabulated x2=3.841. Hence, there is enough evidence to reject our null hypothesis and imply that the blood pressure is dependent on the type of job.

Another Statistical Test

We perform a normal test to determine if there is a significant dispersion from the normal value of blood pressure for an adult at rest which is 120 for the systolic and 80 for diastolic.

We perform a Z-test to establish whether the difference in means is significant.

The descriptive statistic of the systolic and diastolic:

 Systolic Diastolic Sum 3969 2453 Mean 136.8621 84.58621 Variance 222.769 171.9782 Standard Deviation 14.92545 13.11404

Z=x-mSn the hypothesis:

Ho: There is no sidnificant difference between the blood pressure at rest and the mean blood pressure for the different type of jobs.

Ho: There is a significant difference between the blood pressure at rest and the mean blood pressure for the different type of jobs.The calculated Z static

Z=x-mSn=136.8621-12014.9254529=6.0839, for systolicZ=x-mSn=84.58621-8013.1140429=1.883, for diastolic 95% confidence level tabulated Z-value from standard normal tables is 1.96.

Conclusion

For Systolic Pressure

Tabulated Z-value<Calculated Z-value

We reject the null hypothesis. Hence we imply there is a significant difference in the systolic blood pressure for an adult at rest that of an adult doing a particular type of job.

For the Diastolic Pressure

Tabulated Z-value> Calculated Z-value

We do not reject the null hypothesis. Hence we imply there is no significant difference in the diastolic blood pressure for an adult at rest that of an adult doing a particular type of job.

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