A researcher for the Department of Justice conducts a survey to estimate the attitudes of South Africans to the introduction of the death penalty. The researcher measures attitudes on a scale that...

A researcher for the Department of Justice conducts a survey to estimate the attitudes of South Africans to the introduction of the death penalty. The researcher measures attitudes on a scale that ranges from strongly opposed (–10) through neutral (0) to strongly in favour (+10). The survey reveals that the scores on the attitude scale were normally distributed, with a mean of 5 and a standard deviation of 13. Assume that these are population values. The researcher is also aware that the population in Cape Town appears to be more vocal about the disadvantages of the death penalty than people from other cities. They decide to conduct the very same attitude survey on a random sample of 100 Capetonians, and discover that the mean score is 1.

a) Test the hypothesis that Capetonians have a different attitude to other South Africans regarding the introduction of the death penalty (α = 0.01).

b) Are Capetonians more opposed to the death penalty than other South Africans (α = 0.01)?

c) What is the chance of making a Type I error in the above tests?

d) How would the chance of making Type I and Type II errors change if we changed the significance level to α = 0.05?

e) If the researcher conducts the survey on a random sample of 50 Capetonians, would they still find that there is a difference between their attitudes and those of other South Africans (α = 0.01)?