Question

Beta endorphins are morphine like substances produced by the body. They create a sense of well-being. It has been proposed that Beta endorphins increase with exercise. Sport scientists conducted an experiment to investigate this problem. They used R to perform a hypothesis test and adopted a significance level of 0.05. The differences (dif) were computed as follows:

dif = Beta-endorphins post-test minus Beta-endorphins post-test

The following R output was generated. Look at the R output generated. Answer each question below assuming the assumptions associated with this procedure are valid.

## 
##  One Sample t-test
## 
## data:  z$dif
## t = 6.8419, df = 8, p-value = 6.604e-05
## alternative hypothesis: true mean is greater than 0
## 95 percent confidence interval:
##  11.51382      Inf
## sample estimates:
## mean of x 
##  15.81111

(2a)
How many athletes took part in both the pre- and post-measurements?

(2b)
Explain how the number 15.81111 was computed.

(2c)
Formulate a null and alternate hypothesis in symbols and words.

(2d)
What is the value of the test statistic?

(2e)
Draw a picture that shows the test-statistic and critical t-value(s).

(2f)
State the conclusions of the test for an expert and non-expert audience.

Answer 1