Question

1. Heart rate during laughter. Laughter is often called “the best medicine,” since studies have shown that laughter can reduce muscle tension and increase oxygenation of the blood. In the International Journal of Obesity (Jan. 2007), researchers at Vanderbilt University investigated the physiological changes that accompany laughter. Ninety subjects (18–34 years old) watched film clips designed to evoke laughter. During the laughing period, the researchers measured the heart rate (beats per minute) of each subject,
   with the following summary results:

• Mean = 73.5,
• Standard Deviation = 6.
• n = 90 (we can treat this as a large sample and use z)

It is well known that the mean resting heart rate of adults is 71 beats per minute. Based on the research on laughter and heart rate, we would expect subjects to have a higher heart beat rate while laughing.

Construct 95% Confidence interval using z value. What is the lower bound of CI?

1. Calculate the value of the test statistic.(z*)
2. If alpha = 05, find the critical value of the rejection region for this test.
3. What is your conclusion in regards to the Null Hypothesis?

Answer 1

Solution: Given sample size 'n' = 90, Mean= 73.5, standard deviation = 6

The 95% confidence interval formula is given by

where ,

The confidence bounds(limits) obtained using the above formula are 72.3(lower bound) and 74.7(upper bound)

The lower bound of the CI is 72.3.

a. We can apply the Z-test for single mean

There is no significant difference in the heartbeat counts before and after viewing of film clips for evoking laughter

There is an increase in heartbeat counts after viewing of film clips for evoking laughter. (right tailed test)

The Z-test statistic for testing single mean is given by

where =73.5, =71, =6, n= 90

Therefore, Z= 3.9582847

b. The critical value for alpha= 0.05 is 1.65

c. for a right tailed test, if , then we accept the null hypothesis,

here, for the given problem,  , 3.9582847 > 1.65,

Therefore we reject the null hypothesis and conclude that laughter improves heart beat rate.

Hope the answer helped you.