Question

In a given sport, it is considered doped if the concentration of a particular substance exceeds 160 µg / ml. At one athlete in the sport 4 measurements were made and the results are shown in the table

Measurement 1	Measurement 2	Measurement 3	Measurement 4
160	156	158	171

You can assume that the concentration is normally distributed and that the standard deviation is σ = 7
a) Set up the null hypothesis and the hypothesis to test if the practitioner is doped.
b) Make the test at the significance level of 5%. Don't forget to conclude the test
c) Suppose the practitioner is doped so that the practitioner's actual µ is 166µg / ml.
Calculate the probability that the practitioner does not get caught in the doping control

Answer 1

a) We need to conduct the One-sample, Right-tail test for dfference of mean, when population standard deviation is known

b) We need to compute the test statistic based on given data and make a conclusion

Measurements: 160, 156, 158, 171

Conclusion: Observed statistic does not fall in the critical range, i.e. 0.357 is less than the critical value 1.645. Hence, we fail to reject the null hypothesis and conclude that practitioner is not doped

c) We first need to find the rejection regions

We need to find the probability of type II error when the true mean is 166. This corresponds to the observed mean falling in the acceptance range, as obtained from above