Question 1

Use the information in the dataset AIS.sav to answer the following questions. The data set AIS.sav contains information that was collected as part of a comprehensive study on 102 male and 100 female athletes randomly selected from the Australian Institute of Sport. Consider the data set as a random sample of all athletes of the Australian Institute of Sport (AIS).

You should use SPSS to calculate the sample statistics you will need to do this question, but for the confidence interval in part (a) and test statistic in part (d) you are required to do the rest of the calculations by hand, using a calculator.

(a) Find a 99% confidence interval for the population mean BMI of all the athletes of AIS by hand (show all working). [You may use sample summary statistics from SPSS outputs without pasting the outputs in your answer.]

(b) Check the appropriate conditions and assumptions needed for the validity of the confidence interval or hypothesis test for the population mean BMI of all the athletes of AIS (include an appropriate graph to support your answer).

(c) A doctor suspects that the average BMI of the population of AIS athletes is more than 22 kg/cm2. State appropriate hypotheses (define any symbols used) to perform a hypothesis test to see if there is evidence to support the suspicion, based on the available BMI data (regardless of whether the conditions in part (b) are satisfied or not).

(d) Calculate the value of the appropriate test statistic for testing the hypotheses in part (c).

(e) Based on the test statistic calculated in part (d) and using the appropriate statistical table provided in the StudyDesk, find the P-value of the test, and write a meaningful conclusion at the 1% level of significance.

(f) Now, check your answers for parts (d) and (e) by finding the value of the test statistic and the P-value using SPSS. Include SPSS output in your answer and comment on the comparison with the hand calculated values. Explain any differences.

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