Data Analysis

DATA ANALYSIS
STUDENT ID:
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Question 1
(a) Population mean of heart rate of critically ill patients survived cardiac arrest = 104.97
98% confidence interval =?
Mean = 104.97
Standard deviation = 29.441
Sample size = 88 (Survival 1)
Standard error =29.441/ sqrt (88) = 3.138
Degree of freedom = 88-1 = 87
The t value for 98% confidence interval = 2.369
It is noteworthy that t value has been used since the population standard deviation is
unknown.
Margin of error = t value * standard error = 3.138 = 7.4339
Lower limit = Mean – Margin of error = 104.97 - 7.4339 = 97.53
Upper limit = Mean + Margin of error =104.97 + 7.4339 = 112.4
98% confidence interval = [97.53 112.4]
(b) Normal probability plot heart rate of critically ill patients survived cardiac arrest
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Based on the above plots, it is apparent that the underlying variable of interest can be
assumed to be normally distributed.
(c) Null and alternative hypotheses
H0: μ <= 90 i.e. the mean heart rate for critically ill patients admitted to hospital in cardiac
arrest who survived is not higher than that of the overall population
Ha: μ > 90 i.e. the mean heart rate for critically ill patients admitted to hospital in cardiac
arrest who survived is higher than that of the overall population
(d) The test statistics computation is shown below.
t stat = (Sample mean – Hypothesised mean)/Standard Error
t stat= 104.97−90
3.138
t stat=4.77
(e) The p value computation is shown below.
Sample size = 88 (Survival 1)
Degree of freedom = 88-1 = 87
The p value = 0.00001 (based on relevant tables and df)
Significance level = 0.01
It can be seen that the p value is lower than the significance level and hence, sufficient
evidence is present to reject the null hypothesis and to accept the alternative hypothesis.
Therefore, it can be concluded that the average heart rate of adults is more than 90 beats per
minutes. Hence, it would be correct to conclude that the mean heart rate for critically ill
patients admitted to hospital in cardiac arrest who survived is higher than that of the overall
population.
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