Inference for Proportions Review

Which of the following is the most appropriate interval for the manager to use for such an estimate?

• A

• B

• C

• D

• E

A town council wants to estimate the proportion of residents who are in favor of a proposal to upgrade the computers in the town library. A random sample of 100 residents was selected, and 97 of those selected indicated that they were in favor of the proposal. Is it appropriate to assume that the sampling distribution of the sample proportion is approximately normal?

• A

• B

• C

• D

• E

A hypothesis test was conducted to investigate whether the population proportion of students at a certain college who went to the movie theater last weekend is greater than 0.2. A random sample of 100 students at this college resulted in a test statistic of 2.25. Assuming all conditions for inference were met, which of the following is closest to the p-value of the test?

• 0.0061

• 0.0122

• 0.0244

• 0.9756

• 0.9878

Consider a 90 percent confidence interval constructed to estimate the difference between two population proportions. Which of the following is the best interpretation of what is meant by 90 percent confidence?

• The probability that the true difference in population proportions falls within the bounds of the confidence interval is 0.90.

• For repeated random sampling from the populations with samples of the same size, approximately 90% of the sample proportions will fall within the bounds of the confidence interval.

• If the sampling process is repeated 10 times, 9 intervals will capture the true difference between the population proportions and 1 interval will not.

• For repeated random sampling from the populations with samples of the same size, approximately 90% of the confidence intervals constructed will capture the true difference between the population proportions.

• For repeated random sampling from the populations with samples of the same size, approximately 90% of the confidence intervals constructed will capture the sample difference between the population proportions.

In the United States, 36 percent of the people have a blood type that is A positive. From a random sample of 150 people from Norway, 66 had a blood type that was A positive. Consider a hypothesis test to investigate whether the proportion of people in Norway with a blood type of A positive is different from that in the United States. Which of the following is the standard deviation used to calculate the test statistic for the one-sample z-test?

• A

• B

• C

• D

• E

In a hypothesis test for a single proportion, which of the following is assumed for the calculation of the p-value?

• The alternative hypothesis is true.

• The null hypothesis is true.

• The distribution of the population is approximately normal.

• The sample proportion is equal to the hypothesized proportion.

• The sample size is 30 or more.

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

• z = 1.645

• z = 1.96

• z = -1.645

• z = -1.96

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 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 of 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 of 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 of 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%.

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)