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 would be the proper set of hypotheses?

Group of answer choices

A. H0: μ = 139, H1: μ ≠ 139
B. H0: μ = 140, H1: μ < 140
C. H0: μ = 140, H1: μ ≠ 140
D. H0: μ = 139, H1: μ < 139

Answer 1

Answer:

Option B)

$H_{0}: \mu = 140\text{ mm}\\H_A: \mu < 140\text{ mm}$

Step-by-step explanation:

We are given the following in the question:

Hypothesis:

The doctors and u=instructor claims that practicing yoga reduces blood pressure and hence is beneficial to people.

Population mean, μ =  140 mm

Sample mean, $\bar{x}$ =  139 mm

Sample size, n = 51

Sample standard deviation, s = 5 mm

Thus, we can design the null hypothesis and alternate hypothesis as

$H_{0}: \mu = 140\text{ mm}\\H_A: \mu < 140\text{ mm}$

The null hypothesis states that the population have a blood pressure of 140 mm. The alternate hypothesis states that yoga reduces the blood pressure and the sample has a blood pressure less than 140 mm.

Thus, the correct answer is

Option B)

$H_{0}: \mu = 140\text{ mm}\\H_A: \mu < 140\text{ mm}$