A recent random poll was taken to estimate the proportion of Australians ...

  

A recent random poll was taken to estimate the proportion of Australians who are in favour of a price on carbon emissions. Of the 375 people in the sample, 129 reported they were in favour of a price on carbon.

a) Using the sample information, compute the 95% confidence interval for the proportion of Australians who are in favour of a price on carbon emissions. (3 marks)

b) Interpret the confidence interval. (2 marks)

c) If the width of the 95% confidence interval was required to be no more than 0.04, what sample size would be required? (2 marks)  

d) The Australian newspaper recently reported that 32% of Australians were in favours of a price on carbon emissions in 2011. Assuming the report to be correct, undertake a hypothesis test to determine whether the population proportion of Australians has increased since 2011. Use a 5% level of significance. (5 marks)

e) If 34% of Australians now support a price on carbon, what type of error (if any) was made in part (d)? Explain.