Question 2

Considering the data set AIS.sav is a random sample of all athletes of the Australian Institute of Sport (AIS) population answer the following questions. You should use SPSS to calculate any sample summary statistics you will need to do this question, but for parts (d)-(g) you are required to do the rest of the calculations by hand, using a calculator and statistical tables.

From previous studies it was known that the proportion of women athletes with medium level of Plasma Ferritin concentration (50ng/mL - 120ng/mL) was 0.35. A doctor claims that the proportion of women athletes with medium level of Plasma Ferritin concentration has increased in recent times.

(a) What is the variable of interest here?

(b) State the appropriate hypotheses (define any symbols used) to test the doctor’s claim that the proportion of women athletes with medium level of Plasma Ferritin concentration has increased in recent times.

(c) Check the conditions and assumptions for the validity of the hypotheses to be tested in part (b).

(d) Calculate the value of the appropriate test statistic for testing the hypotheses in part (b). [You only need to work with the women athletes with medium level of plasma ferritin here.]

(e) Using the appropriate statistical table provided in the StudyDesk, find the P-value for the test, and write a meaningful conclusion at the 5% level of significance in the context of this study.

(f) If the doctor wants to be 95% confident that the margin of error of the estimate of the true proportion of women athletes at AIS with medium level of Plasma Ferritin concentration is within 0.06, what minimum sample size is required? For calculations, use an estimated proportion from the given data.

(g) If the doctor decides to use a conservative method (approach), what will be the minimum sample size to keep the same level of confidence and margin of error as in part (f)? What is the impact on the sample size of this decision? (Include evidence to support your answer).

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