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Owner: deppek1
Created: Feb 12, 2011
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Results in this report
1. Histogram of Cholesterol Levels for Primary Hypertensive (PH) and for Normotensive (NT) and
2. summary Statistics cholesterol
3. Two sample T statistics with data for Cholesterol with pooled variance
4. Two sample T statistics with cholesterol data CI at 95%
 
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A Comparison of the Cholesterol Levels for A Sample of Patients with Primary Hypertension and a Sample of Patients who are Normotensive
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Researchers would like to compare the mean cholesterol level for a sample of patients with primary hypertension and a sample of patients who are normotensive.  To do this, a random sample of 133 patients with primary hypertension (PH) had their cholesterol measured and recorded.  Similarly, a random sample of 41 normotensive (NT) patients had their cholesterol measured and recorded. 

The null hypothesis to be tested is that the mean cholesterol level is the same for those with primary hypertension and those who are normotensive against an alternative of some difference in cholesterol levels existing for those with primary hypertension and those who are normotensive.  The null hypothesis will be tested at the 0.05 level of significance.

Histograms for the two groups were created to compare the distribution of cholesterol levels for each group.  Results 1 shows the histograms.

Result 1: Histogram of Cholesterol Levels for Primary Hypertensive (PH) and for Normotensive (NT) and   [Info]
Right click to copy

From the histograms created, one can see that the distributions are roughly symmetric and mound-shaped.  Further, since samples are greater that 40, we will proceed under the assumption the cholesterol level for those with primary hypertension and those who are normotensive are approximately  normally distributed.

The following assumptions for proceeding with t-test are met:

  • the data are interval/ratio data
  • the samples are independent, not paired and random
  • the histograms show normally distributed data
  • looking at the standard deviation in the summary statistics in Results 2, if we double the smaller standard deviation (29.655798 * 2 = 59.311596) and compare this result to the largest standard deviation 33.044834, the value is larger and this indicates the variance can be assumed to be equal and no modification in the t-test is needed.

Result 2: summary Statistics cholesterol   [Info]
Summary statistics:
Column n Mean Variance Std. Dev. Std. Err. Median Range Min Max Q1 Q3
PH 133 214.70677 879.4664 29.655798 2.5714839 214 167 117 284 199 235
NT 41 193.19513 1091.9609 33.044834 5.160736 194 165 121 286 177 206

Based on the assumptions for the t-test, we will proceed in analyzing the data using t-test with equal variance.

Result 3: Two sample T statistics with data for Cholesterol with pooled variance   [Info]
Hypothesis test results:
μ1 : mean of PH
μ2 : mean of NT
μ1 - μ2 : mean difference
H0 : μ1 - μ2 = 0
HA : μ1 - μ2 ≠ 0
(with pooled variances)
Difference Sample Mean Std. Err. DF T-Stat P-value
μ1 - μ2 21.511644 5.444244 172 3.9512641 0.0001

 At the 0.05 level of signifiance (t =3.9512641, p-value = 0.0001), there is statistically significant evidence to support the claim that patients with primary hypertension have a different mean cholesterol level than those patients who are normotensive.

Given the decision, to accept the alternative hypothesis, one can estimate how much higher the cholesterol level is for those with primary hypertension compared to normotensive patients by calculating a confidence interval.  The results of our confidence level at 95% are presented in Results 4.

Result 4: Two sample T statistics with cholesterol data CI at 95%   [Info]
95% confidence interval results:
μ1 : mean of PH
μ2 : mean of NT
μ1 - μ2 : mean difference
(with pooled variances)
Difference Sample Mean Std. Err. DF L. Limit U. Limit
μ1 - μ2 21.511644 5.444244 172 10.765512 32.25778

With 95% confidence, we estimate that the mean cholesterol level for patients with primary hypertension is between 10.765512 and 32.25778 more than the mean cholesterol level for patients who are normotensive.

 

HTML link:
<A href="http://www.statcrunch.com/5.0/viewreport.php?reportid=17637">A Comparison of the Cholesterol Levels for A Sample of Patients with Primary Hypertension and a Sample of Patients who are Normotensive</A>

Comments
Comment by deppek1 on Feb 12, 2011
Thank you for bringing the problem to my attention. The reason it didn't populate right was due to my using the command rather than the correct exam
Comment by pickensk1 on Feb 12, 2011
For some reason your results did not populate into the report which makes it hard to interpret them. I like the way you bulet-pointed the t test requirments.
Comment by pickensk1 on Feb 12, 2011
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