Means and Proportions Review

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.

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 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

• 0.011

• 0.022

• 0.033

• 0.066

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)

A restaurant manager will randomly select a sample of filled cups each day and measure the volume of liquid in each cup. Past measurements have shown that the standard deviation of liquid dispensed by this machine is 0.2 ounces. An estimate of the mean volume must be reported within a margin of error of 0.1 ounces with 98% confidence. What is the minimum sample size for the number of drinks the manager must select?

• 2

• 5

• 16

• 17

• 22

A nutritionist claims U.S. children drink an average of less than 2 glasses of milk per day. Based on an SRS of 30 children, the p-value of H₀: μ = 2 vs. H_A: μ < 2 is 0.0015. What is the correct interpretation of the p-value?

• The probability that she fails to reject the null hypothesis is 0.015%

• The probability that she rejects the null is 0.015%

• She can be 99.85% confident that the alternative hypothesis is true

• About 0.15% of all samples would product a test statistics at least as extreme as ours if the null hypothesis is true.

• About 99.85% of all samples would product a test statistics at least as extreme as ours if the null hypothesis is true.

USA Today reported that in 1992, 39% of all elementary school children claimed that when they grow up they want to do something to help other people. However, in 1995, 128 of a random sample of 317 of these same children claimed that when they grow up they want to do something to help other people. Does this information indicate that there has been an attitude change either way?

• One-Sample Z Test for a Proportion

• Two-Sample Z Test for the Difference in Proportions

• One-Sample T Test for a Mean

• Two-Sample T Test for the Difference in Means

In 1975, a random sample of 1484 adult U.S. citizens was surveyed, and 193 strongly agreed with the statement, "People should take care of themselves". Then, in 1991, a survey of 1013 adult U.S. citizens showed that only 61 strongly agreed with the statement. Does this indicate that the proportion of U.S.adults who strongly agree with the given statement has dropped?

• Two-Sample Z Test for the Difference in Proportions

• Two-Sample T Test for the Difference in Means

• Matched Pairs T Test for a Mean

• One-Sample T Test for a Mean

Suppose that in a sample of 36 bottles from a certain bottling machine, the machine filled the bottles with an average of 16.1 ounces of cola. The sample had a standard deviation of 0.11 ounces. Give a 90% confidence interval for the mean number of ounces.

• Proportion Z-Test

• Sample T-Test

• Sample T-Interval

• Proportion Z-Interval

What does the symbol represent?

• mean from a sample

• proportion from a population

• standard deviation of the sampling distribution of sample proportions

• mean of the sampling distribution of sample proportions

• mean from a population