Question

The population of male industrial workers in London who have never experienced a major coronary event has mean systolic blood pressure 136mmHg diastolic blood pressure 84mmHg. We are interested in determining whether these values are the same as those for the population of industrial workers who have suffered a coronary event. Show all work.

a.A sample of 86 workers who have experienced a major coronary event has mean systolic blood pressure of 143mmHg and standard deviation s=24.4 mmHg. Test whether these workers have the same mean systolic blood pressure as those who have not experienced a major coronary event.

b.The sample of 86 workers has mean diastolic blood pressure of 87mmHg and standard deviation s=16.0 mmHg. Test whether or not these workers have the same mean diastolic blood pressure as those who have not experienced a major coronary event.

Answer 1

Since population standard deviation is unknown so we need to use t test.

a)

Hypotheses are:

Here we have following information:

So test statitics will be

Here test is two tailed and degree of freedom of the test is df=n-1=86-1=85.

The p-value using excel function "=TDIST(2.66,85,2)" is 0.0093.

Since p-value is less than 0.05 so we reject the null hypothesis. That is we cannot conclude that  these workers have the same mean systolic blood pressure as those who have not experienced a major coronary event.

b)

Hypotheses are:

Here we have following information:

So test statitics will be

Here test is two tailed and degree of freedom of the test is df=n-1=86-1=85.

The p-value using excel function "=TDIST(1.739,85,2)" is 0.0857.

Since p-value is greater than 0.05 so we fail to reject the null hypothesis. That is we can conclude that these workers have the same mean diastolic blood pressure as those who have not experienced a major coronary event.