Question

The Australian Government is interested in the proportion of people who are either Satisfied or Very Satisfied with current Government Climate Change policies. They believe that they have the support of the majority of Australians.

You are to conduct a hypothesis test to check their Claim. The random sample of 400 customers shows that 225 people were either Satisfied or Very Satisfied with the current Government policies.

Write down the Null and Alternative hypotheses in both Symbols and Words for the above situation.

For the Hypothesis Test above, use a level of significance (α) of 5% when answering the following questions.

i. What is the critical value(s)?

ii. State your decision rule?

For the Hypothesis Test above, calculate the value of the test statistic.

For the Hypothesis Test above, state your decision then, in plain language, your conclusion. Explain your reasoning.

Based on your answer to Question 14, would the p-value be less than 5%? Explain why/why not.

With hypothesis testing, there is always the risk that you will reach an incorrect conclusion. Based on your answer to Question 14, what type of error (Type I or Type 2 error) could be made here? Explain what this means in the context of the Australian Government’s claim.

Answer 1

Hypothesis:

The proportion of people who are either Satisfied or Very Satisfied with current Government Climate Change policies is less than or equal to 50%.

The proportion of people who are either Satisfied or Very Satisfied with current Government Climate Change policies is greater than 50%.

i.

Critical value = 1.645

ii.

Decision rule: If calculated value of test statistic is greater than critical value, we reject null hypothesis.

iii.

Sample proportion:

Test statistic,

Since calculated value of test statistic is greater than critical value, we reject null hypothesis. And conclude that majority of Australians are either Satisfied or Very Satisfied with current Government Climate Change policies.

Type I error : Probability of rejecting H_0, when it is true.

Type II error : Probability of accepting H₀, when it is false.

Here we reject null hypothesis, this means we may commit type I error.

This means that proportion of people who either Satisfied or Very Satisfied with current Government Climate Change policies is less than or equal to 50% and we consider it is greater than 50%.