STA2300 Data Analysis - Tutoring 2

Question 2 (25 marks)
The dataset Body.sav is a random sample from the population of California health and fitness clubs. To answer the following questions you should use SPSS to calculate any sample 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 females in all the California health and fitness clubs was 0.45. A sport health specialist claims that the proportion of females in all California health and fitness clubs has increased in recent times.

1. (1 mark) What is the variable of interest here?
2. (3 marks) State the appropriate hypotheses (define any symbols used) to test the specialist’s claim that the proportion of female participants has increased in recent times.
3. (4 marks) Check the conditions and assumptions for the hypotheses to be tested in part (b).
4. (4 marks) Calculate the value of the appropriate test statistic for testing the hypotheses in part (b).
5. (4 marks) 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.
6. (5 marks) If the sport health specialist wants to be 99% confident that the margin of error of the estimate of the true proportion of female participants is within 0.04, what minimum sample size is required? For calculations, use an estimated proportion from the given data.
7. (4 marks) If the sport health specialist 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 of this decision? (Include evidence to support your answer).