Assignment 2

Due Date:                            08 October, 2020

Weighting:                         20%

Full Marks:                          100 (final marks to be converted to 20%)

• Answering the questions in this assignment should not be your first attempt at these types of It is essential that you work through practice exercises from the tutorial sheets in the Study Book and/or Text Book first.
• This assignment is important in checking your knowledge, providing feedback and helping to establish competency in essential
• Answer all the The questions are not of equal weight; some questions are worth much more than the others.
• The questions relate to materials up to and including Module
• Before starting this assignment read Notes Concerning Assignments under the Introductory Material link in the ‘Getting started’ tab on the StudyDesk.
• When you are asked to comment on a finding, usually a short paragraph is all that is
• Do not copy/paste SPSS output into your assignment unless specifically asked to do so. In many cases the SPSS output contains much more information than is required for a correct and complete answer. In those cases just reproducing the output may not attract any marks. Make sure you report only the information from the SPSS output relevant to your answer.
• In order to obtain full marks for any question you must show all working. No working, no
• Convert your word document to pdf before submitting your assignment via the link on the StudyDesk. See the Introductory Material (Section 5, Assignments) for information about how to do this properly.
• This assignment consists of 5 questions.
• It is vitally important that you understand USQ policies and procedures, in particular those related to communication, assessment, academic integrity and plagiarism. Details are under the Assessment link on the
• You will need to download data set sav from the StudyDesk of the course. Detailed information on the variables in the data set is found in Body.txt file accessible from the StudyDesk.

Question 1      (25 marks)

This question uses information from the data file Body.sav found under the Assessment tab on the StudyDesk (also see Body.txt for more details about the source and the variables reported in the dataset). Make sure the Variable View in SPSS is setup properly with all ‘labels’ correctly defined (with units), all ‘values’ assigned correctly for categorical variables and the correct ‘measure’ selected for all variables.

The participants in the Body.sav dataset were taken randomly from dozens of California health and fitness clubs and the measurements were taken by technicians under the supervision of one of the researchers.

You should use SPSS to calculate the sample statistics (eg., mean and standard deviation) 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.

• (8 marks) Construct a 99% confidence interval for the population mean Chest depth between spine and sternum (cm) of the participants in the age category “20 years and under” of all the California health and fitness clubs by hand (show all working).
• (5 marks) Check the appropriate conditions and assumptions needed for the validity of the confidence interval or hypothesis test for the population mean Chest depth between spine and sternum (cm) of the participants in the age category of “20 year or under” of all the California health and fitness clubs (include an appropriate graph to support your answer).
• (3 marks) A sports health specialist suspects that the average mean Chest depth between spine and sternum (cm) in the age category “20 years or under” of the California health and fitness clubs is more than 17cm. 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 data (regardless of whether the conditions in part (b) are satisfied or not).
• (2 marks) Calculate the value of the appropriate test statistic for testing the hypotheses in part (c).
• (4 marks) 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.
• (3 marks) 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

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 mark) What is the variable of interest here?
• (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.
• (4 marks) Check the conditions and assumptions for the hypotheses to be tested in part (b).
• (4 marks) Calculate the value of the appropriate test statistic for testing the hypotheses in part (b).
• (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
• (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 04, what minimum sample size is required? For calculations, use an estimated proportion from the given data.
• (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).

Question 3     (16 marks)

In this question, consider the data on the Waist girth and Navel girth of the California health and fitness clubs from the dataset Body.sav. The fitness specialists believe that the Waist girth of the California health and fitness clubs’ population is not different from their Navel girth. To find out if the mean Waist girth of the California health and fitness clubs’ population is different from that of their Navel girth, they wish to perform appropriate statistical analyses.

• (3 marks) State appropriate hypotheses (define any symbols used) to perform an appropriate statistical
• (2 marks) State (but do not check) the assumptions required for the validity of the Describe the assumptions in the context of the study.
• (3 marks) Without using SPSS, calculate the value of the appropriate test statistic to test the hypotheses in part (a). [You can use appropriate sample statistics (e.g., mean and standard deviation) from SPSS output for ]
• (2 marks) Using the appropriate statistical table provided in the StudyDesk, determine the P- value of the above test.
• (3 marks) Based on the P-value describe the outcome of the test in the context of the
• (3 marks) Now use SPSS to carry out the test. Copy and paste the relevant SPSS output to your assignment Do these results agree with those found in part (e)? (Hint: comment on the test statistic, P-value and conclusion).

Question 4     (20 marks)

Use the information on the Knee girth over patella (cm) and Gender of the California health and fitness clubs from the dataset Body.sav to answer the following questions. You should use SPSS to calculate any sample statistics (eg., mean and standard deviation) you will need to do this question, but for part (e) you are required to do the rest of the calculations by hand, using a calculator.

The fitness specialists wish to check if the mean of the Knee girth over patella (cm) of California health and fitness clubs’ female participants is lower than that of the male participants.

• (4 marks) Using SPSS produce an appropriate graph to compare the distribution of Knee girth over patella (cm) of the female and male participants of California health and fitness Label the axes correctly, include unit of measure and provide an appropriate title which includes your name.
• (2 marks) Using the graph produced in part (a), briefly describe the distribution of Knee girth over patella for the two groups of (male and female) participants. Features discussed should include the shape, centre, spread and outliers, if
• (3 marks) State appropriate hypotheses (defining all symbols) to answer the question: ‘Is the mean Knee girth over patella of female participants is less than that of the male participants?’
• (2 marks) State (but do not check) the assumptions required for the validity of the Describe the assumptions in the context of the study.
• (2 marks) Without using SPSS, calculate the value of the appropriate test statistic for testing the hypotheses in part (c). [You can use appropriate sample statistics from SPSS output for ]
• (4 marks) Using the appropriate statistical table provided in the StudyDesk, find the P-value of the test, and describe the outcome of the test in the context of the
• (1 mark) Now use SPSS to check your results for the above hypothesis Run the appropriate test procedure in SPSS, and then copy and paste the relevant output for this test into your assignment.
• (2 marks) Briefly comment on how the test statistic and P-value from SPSS output are similar to or differ from your hand

Question 5     (14 marks)

The daily travelling time of the staff of a large corporation to come to the office is a random variable. Based on the historical record on the travelling time of the staff over the years it is found that the mean and standard deviation of daily travelling time are 35 minutes and 6 minutes respectively. Assume that the distribution of the daily travelling time of the staff follows a normal model. For a random sample of the daily travelling times of 9 staff, answer the following questions.

• (1 mark) What is the variable of interest in the question?
• (3 marks) Find the probability that the randomly selected daily travelling time of one member of staff will be less than 32
• (3 marks) What type of distribution is the sampling distribution of sample mean of the daily travelling time? Specify the parameters of this distribution for a random sample of the daily travelling times of 9 staff of the corporation, and write the values of those parameters in this

(d)   (5 marks) Find the probability that the sample mean of the random sample of daily travelling times of 9 staff will be less than 32 minutes.

• (2 mark) Explain the reason for the difference in your answers in parts (b) and (d).