Question

Cholesterol levels are measured for 28 heart attack patients (2 days after their attacks) and 30 other hospital patients who did not have a heart attack. It is thought that cholesterol levels will be higher for the heart attack patients, so a one-sided alternative hypothesis is used. For the 28 heart attack patients, the mean cholesterol level was 253.9 with a standard deviation of 47.7. For the 30 other hospital patients who did not have a heart attack, the mean cholesterol level was 193.1 with a standard deviation of 22.3. At 3% SL, is there any difference between those two groups? Apply one-sided test.

Answer 1

As we are testing here whether the cholesterol levels will be higher for the heart attack patients, therefore the null and the alternative hypothesis here are given as:

The standard error here is computed as:

The test statistic here is computed as:

As the t statistic value here is very high, therefore the approximate p-value here is 0. Therefore 0 is the required p-value here. As the p-value is 0 < 0.03 which is the level of significance, therefore the test is significant and we can reject the null hypothesis here. Therefore we have sufficient evidence that the cholesterol levels will be higher for the heart attack patients.