Question

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

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.

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

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

5. Based on your answer to Question 4, 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 Q4, what type of error (Type I or Type 2 error) could be made here? Explain what this means in the context of the Government’s claim.

2. 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?

Answer 1

Since we want to test if the majority are satisfied or very satisfied, we want to know if more than 50% are happy

(1) The Hypothesis

H0: p < 0.5 : The proportion of people who are satisfied or very satisfied with the present Government change policies is at most 0.5.

Ha: p > 0.5: The proportion of people who are satisfied or very satisfied with the present Government change policies is greater than 0.5.

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(2) The critical value at = 0.05 (right tailed) is 1.645

The Decision Rule: If Z test is > 1.645, Then Reject H0.

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(3) The Test Statistic: = 225/400 = 0.5625

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(4) The Decision: Since z test is > 1.645, Reject the Null Hypothesis

The Conclusion: There is sufficient evidence at the 5% significance level to conclude that the the majority of people are satisfied or very satisfied with the current Government change policies.

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(5) Yes, The p value would be less than 5%. This is because we have rejected H0 on the basis that the test statistic is being greater than the critical value approach. Using the p value approach, we would reject H0, if the p value is < (0.05). Since the test statistic is in the rejection region it means that the p value also would be in the rejection region i.e it would be less than 5%. (The p value from the standard normal tables is 0.0062, which is less than 5% )

Type of Error: Since we are rejecting the null hypothesis, we could be making a Type I error here. (A type I error is the incorrect rejection of a true null hypothesis).

This means that it could be possible that the majority are not satisfied with the current Government change policies but they think that the voters are satisfied, when they actually are not. This would make the Government feel that everything is fine, wand not not make the requisite changes, which could cost them the next election.

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