# a. Use three graphical techniques to present the information.

01 / 10 / 2021 Statistics

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The following table indicates the geographic location of share ownership for selected years

Refer to diagrams A, B and C. Describe the three types of correlations shown below.

in five Australian states.

a. Use three graphical techniques to present the information.

b. Explain the four components of time series using this set of data.

c. Describe any general or specific trends observed over time.

d. Is a linear trend appropriate? Explain your answer.

e. Across the different states, are there any distinct differences? Explain your view.

f. Half the population in most states including Victoria have share ownership. Test this

hypothesis for the state of Victoria with share ownership percentage value in 2010.

2The following table indicates the P/E ratios and Dividend yields of twenty shares listed on

the Australian Stock Exchange.

What are the measures of variability?

b. Which ones (at least three) would you choose to use to analyse the central values in this

set of data? Explain why.

c. What are the values of the mean and standard deviation of the P/E ratio and dividend

yield?

d. In this list of shares, what are the sampling bias or errors? Name at least two and

provide some detailed explanations.

Refer to diagrams A, B and C. Describe the three types of correlations shown below.

f. Describe the correlation between P/E ratio and dividend yield.

g. State the linear relationship between P/E ratio and dividend yield. Interpret the slope and

the y intercept.

h. Find the value of the coefficient of determination. Interpret the value.

3. An infinite population has a mean of 120 and a standard deviation of 44. A sample of 100

observations is to be selected at random from the population.

a. What is the expected value of the sample mean?

b. What is the standard deviation of the sample mean?

c. What is the shape of the sampling distribution of the sample mean?

d. What does the sampling distribution of the sample mean show?

A researcher conducted a survey on a university campus for a sample of 64 third-year

students. In the past it was reported that third-year students read an average of 3.12 books in

the prior academic semester, with a standard deviation of 2.15 books. Determine the

probability that the sample mean is:

e. less than 3.45.

f. between 3.38 and 3.58.

g. above 2.94.

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