Estimating a Population Proportion

The margin of error (E) in a confidence interval calculation is determined by which of the following?

• Sample size and standard deviation

• Critical value and standard error

• Sample mean and population mean

• Population proportion and sample proportion

Answer explanation

The margin of error (E) in a confidence interval calculation is determined by the critical value and standard error.

A recent study of 750 Internet users in Europe found that 35% of Internet users were women. What is the 95% confidence interval of the true proportion of women in Europe who use the Internet?

• 0.321 < p < 0.379

• 0.316 < p < 0.384

• 0.309 < p < 0.391

• 0.305 < p < 0.395

A sample of 400 racing cars showed that 80 cars cost over $700,000. What is the 99% confidence interval of the true proportion of cars costing over $700,000?

• 0.001 < p < 0.005

• 0.566 < p < 0.693

• 0.148 < p < 0.252

• 0.023 < p < 0.045

In a survey of 104 students, it was found that 79 went to the homecoming game this year. Calculate a 99% confidence interval for p.

• (0.652, 0.868)

• (0.691, 0.829)

• (0.678, 0.842)

• (0.685, 0.895)

In a survey of 104 students, it was found that 79 went to the homecoming game this year. A 99% confidence interval for p is (0.652, 0.868). Interpret this interval.

• 99% of the time the true proportion of people who went to the homecoming game this year is between 65.2% and 86.6%.

• The probability that the population proportion of people who went to the homecoming game this year is between 65.2% and 86.6% is 95%.

• Based on this sample, I am 99% confident that the true proportion of people who went to the homecoming game this year is between 65.2% and 86.6%.

• 99% of all possible intervals calculated this way will capture the true proportion of people who went to the homecoming game this year

Based on the findings from a recent study of Elsik High School Seniors, the class officers created a 90% confidence interval of (0.42, 0.48) to estimate the percent of all Elsik Seniors who are excited about the prom theme. Based on the confidence interval, which of the following claims is NOT supported?

• More than 45 percent of all seniors are excited about the prom theme.

• Approximately 45 percent of all seniors are excited about the prom theme.

• More than 25 percent of all seniors are excited about the prom theme.

• Less than half of all seniors are excited about the prom theme.

A random sample of 100 PHS students found that 53 of them were in possession of a pencil. What is the p-hat for this sample?

• 0.53

• 0.5

• 0.47

• 1

A political candidate is told by his polling organization that a 90% confidence interval for the true proportion of voters who support his candidacy is 0.45 to 0.53. What are the values of the point estimate and margin of error for this interval?

• point estimate = 0.50; margin of error = 0.08.

• point estimate = 0.49; margin of error 0.90.

• point estimate = 0.49; margin of error 0.08.

• point estimate = 0.49; margin of error = 0.04.

• point estimate = 0.49; margin of error cannot be determined without knowing the sample size.

A website asks visitors to vote for which of several user-submitted videos is funniest. After a few days, they have collected 250 votes, and they would like to construct a 95% confidence interval for the true proportion of visitors who prefer one of the videos. However, they recognize that their sampling method involves voluntary response, so the data may be biased. How can they compensate for this problem when constructing their confidence interval?

• Use a lower confidence level, such as 80%.

• Use a higher confidence level, such as 99%.

• Collect an additional 250 votes using an SRS.

• Select a smaller sample.

• Throw this data out. There is no way to compensate for this bias.

If 827 represents "no" voters out of 2584, construct a 95% confidence interval for the "no" group.

• [.300,.340]

• [.298,.342]

• [.302,.338]

• [.288,.352]