Making Inferences About Populations Using Proportions

Which of the following is not a condition that needs to be checked for a significance test when doing inference for a single proportion?

• Ensuring that the sample is independent

• Making sure the sample is representative of the population

• n*p₀ > 10, n*q₀ > 10

• n*p-hat > 10, n*q-hat > 10

z* is the critical value for which of the following tests/intervals?

I. 1-prop. z-test

II. 2-prop. z-interval

III. 1-sample t-test

IV. 2-sample t-interval

• I only

• I and II only

• I, II, and III only

• All of the above

• III and IV only

Which calculator function allows you to find the test statistic for a 2-proportion z-interval?

• normalcdf

• invNorm

• tcdf

• invT

What is the critical value for a 95% confidence interval for proportions?

• z = 1.645

• z = 1.96

• z = -1.645

• z = -1.96

84% of Russians believe that the Sochi Olympics promoted sports development in Russia. The poll of 2,000 people had a margin of error of 2%. What is the best description of what this 2% M.E. means?

• Not all of the 2,000 adults knew something about the Olympics

• About 2% of the 2,000 adults polled refused to answer

• About 2% of adults were expected to change their minds between the time of the poll and its publication time

• The difference between the sample percentage and the population percentage is likely to be less than 2%

• There is a 2% chance that this survey captured the true proportion of Russian adult citizens who would answer yes to the question.

A rubber band man claims that p, the proportion of bands that snap when stretched beyond 8 inches, is no more than 0.03. Some customers have complained that this happens more frequently. Which of the following sets of hypotheses would the customers used to conduct an experiment to test the rubber band man's claim?

• H₀: p ≠ 0.03, H_A: p = 0.03

• H₀: p = 0.03, H_A: p > 0.03

• H₀: p = 0.03, H_A: p ≠ 0.03

• H₀: p = 0.03, H_A: p < 0.03

• H₀: p > 0.03, H_A: p = 0.03

There is a law in ND saying that the ratio of elementary students to teachers can be no more than 22:1. A hypothesis test is performed to determine if the proportion of schools with a ratio above 22:1 is above 25% using an SRS of 85 schools. At the 0.05 significance level, what conclusion can be made if 32 of the schools surveyed exceed this ratio?

• Since the p-value is less than the level of significance level, the null hypothesis should be rejected. There is significant evidence that the true proportion of schools with a higher ratio is more than 25%.

• Since the p-value is greater than the level of significance level, the null hypothesis should be rejected. There is significant evidence that the true proportion of schools with a higher ratio is more than 25%.

• Since the p-value is less than the level of significance level, the null hypothesis should not be rejected. There is not significant evidence that the true proportion of schools with a higher ratio is more than 25%.

• Since p-hat = 0.376 > 0.05, the null hypothesis should not be rejected. There is not significant evidence that the true proportion of schools with a higher ratio is greater than 25%.

• Since p-hat = 0.376 > 0.05, the null hypothesis should be rejected. There is significant evidence that the true proportion of schools with a higher ratio is greater than 25%.

900 men who practice yoga are surveyed to determine if they report low stress levels. The CFO of the surveying company is concerned about the costs associated with surveying 900 men, so she suggests sampling 100 men. Assuming the sample proportion does not change, what effect on the width of the confidence interval would occur in they were to survey 100 men instead of 900?

• The width of the interval based on 100 men would be about 9 times wider than the interval with 900 men.

• The width of the interval based on 100 men would be about 3 times wider than the interval with 900 men.

• The width of the interval based on 100 men would be about the same as the interval with 900 men.

• The width of the interval based on 100 men would be about 1/3 the width of the interval with 900 men.

• The width of the interval based on 100 men would be about 1/9 the width of the interval with 900 men.

In a random sample of 850 city high school students, 768 said they had access to the internet during school hours. 308 of 355 rural high school students said they had access. Which of the following is the p-value for a significance test to determine if these data provide evidence that the proportion of high school students in city areas who have internet access is different than those who go to rural schools?

• 0.002

• 1.2

• 0.09

• 0.033

• None of these is the correct p-value.

Jimmy is interested in comparing the fitness level of the members of his gym to the levels at a competing gym. He randomly selected 125 members of his gym and found 75 passed a fitness test. 70 of 95 at the other gym passed. Which interval estimates, with 96% confidence, the difference in proportion of members in Jimmy's gym who can pass the test and the proportion from the other gym who can pass?

• (-0.2404, -0.033)

• (-0.2602, -0.0135)

• (-0.2661, -0.0076)

• (-0.3490, -0.1099)

• (-0.3547, -0.1042)