Question

The average systolic blood pressure was found to be 140 mm for people who have high responsibility jobs, specifically investment banking jobs. Heart attack is the leading cause of death in the US, and the American Medical Association (AMA) deems average systolic blood pressure of 140 mm as very high. The fitness instructors and AMA doctors recommend practicing Yoga. They believe that practicing yoga reduces blood pressure and hence is beneficial to people. To test this claim, a sample of 51 investment bankers who had previously been diagnosed with high blood pressure was chosen. Participants were trained and completed yoga exercises for six months. At the end of the six months, the average blood pressure for the sample was 139 mm with a standard deviation of 5 mm. What is the actual (i.e. calculated) value of the test statistic?

Answer 1

Answer:

t = -1.428

Step-by-step explanation:

Average blood pressure among people with high responsibility jobs = u = 140 mm

Number of people sampled for the study = n = 51

Average blood pressure of the sample = x = 139 mm

Standard deviation of the sample = s = 5 mm

The claim is that practicing yoga decreases the blood pressure. So we have to test that after practicing yoga, the average blood pressure will be lesser than 140. Based on this we can formulate the null and alternate hypothesis as:

Null Hypothesis: $\mu \geq 140$

Alternate Hypothesis: $\mu < 140$

Since population standard deviation is not known, we cannot use z-distribution for this test. We are given the value of sample standard deviation, so t-test will be used for this case.

Test statistic is calculated as:

$t=\frac{x-u}{\frac{s}{\sqrt{n} } }$

Using the values in this formula gives us:

$t=\frac{139-140}{\frac{5}{\sqrt{51}}}\\\\ t=-1.428$

Therefore, the value of test statistic is -1.428