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Hypothesis Test for a Proportion Example

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Wize University Statistics Textbook > Hypothesis Testing with One Sample

Hypothesis Test for a Proportion

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A survey finds that 64% of Americans in swing states vote for the federal election. We take a random sample of 50 citizens from Ohio, a swing state, and find that 28 of them voted in the 2012 federal election. Is there evidence that voter turnout in Ohio is lower than the average swing state, at the 5% significance level?

State the hypotheses:
Given α=0.05\alpha=0.05, find the corresponding critical value, z*




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Run the test statistic:

z=p^−popoqonz=\frac{\hat{p}-p_o}{\sqrt\frac{p_oq_o}{n}}



Solve for the p-value:


Make your decision:


Draw your conclusion:
We conclude that there is/is no evidence that voter turnout in Ohio is lower than the average swing state.


More Hypothesis Test for a Proportion Questions:
Hypothesis Testing: Proportion
In 2015, 20% of males in the 18-22 age group smoked cigarettes in the
United Kingdom of Perfect Land. The government imposed a sales tax of
30% on the purchase of cigarettes in 2016 to reduce the proportion that smoke.
Hypothesis Testing for a Proportion
HoH_o: The acceptance rate at Wize University is not different than 16%.
HaH_a: The acceptance rate at Wize University is different than 16%.
The critical value CV=1.96CV=1.96
Hypothesis Testing for a Proportion
Margo says she can lower the defect rate of miniature cars in Santa’s Toy Shop to less than 10% by adjusting some machine settings. Her boss will offer her a promotion if there is evidence of this. A random sample of 400 miniature toys was taken from Margo’s unit. They found that 28 were defective.
Which of the following is correct?
Hypothesis Testing for a Proportion
In 2006, it was reported that only 40% of students at the university ask questions in lectures. It is believed that this percentage has changed. You randomly sampled 80 students and asked them "Have you ever asked a question in a lecture?" Twenty-four of them responded "Yes". There are 20,386 students at the university. Use a 5% significance level.
Hypothesis Testing for a Proportion
Parts (i) to (iv) are based on the following information:
In 2006, it was reported that only 40% of students at the university ask questions in lectures. It is believed that this percentage has changed. You randomly sampled 80 students and asked them "Have you ever asked a question in a lecture?" Twenty-four of them responded "Yes". There are 20,386 students at the university.
(i) Find the critical value for a significance level of α=0.05\alpha=0.05.
Hypothesis Testing
Parts (i) to (iii) are based the following information:
Bettina, the general manager for Cornwall Steakhouse, trained her service staff to suggest wine with their customers’ meals. Last month, 55% of customers ordered wine with their meal. A month following the training, she randomly selected 38 receipts. Twenty-six of them included wine sales. Is there evidence that the proportion of customers ordering wine with their meals had increased?
(iii) Select the correct conclusion.
Hypothesis Testing
Parts (i) to (iii) are based the following information:
Bettina, the general manager for Cornwall Steakhouse, trained her service staff to suggest wine with their customers’ meals. Last month, 55% of customers ordered wine with their meal. A month following the training, she randomly selected 38 receipts. Twenty-six of them included wine sales. Is there evidence that the proportion of customers ordering wine with their meals had increased?
(ii) What is the test statistic?
Hypothesis Testing
Parts (i) to (iii) are based the following information:
Bettina, the general manager for Cornwall Steakhouse, trained her service staff to suggest wine with their customers’ meals. Last month, 55% of customers ordered wine with their meal. A month following the training, she randomly selected 38 receipts. Twenty-six of them included wine sales. Is there evidence that the proportion of customers ordering wine with their meals had increased?
(i) Select the correct hypotheses.
Hypothesis Testing a Proportion
Margo says she can change the defect rate of miniature cars in Santa’s Toy Shop by adjusting some machine settings. Her boss will offer her a promotion if this is true. Currently, 10% of the cars are defective. A random sample of 400 miniature toys was taken from Margo’s unit. They found that 28 were defective. At the 5% significance level, will Margo get a promotion?