Estimating a Parameter

In a recent Gallup poll of randomly selected US adults, 75% said they would vote for a law that imposed term limits on members of the US Congress. The poll's margin of error was 4 percentage points at the 95% confidence level. This means that

• the poll used a method that gets an answer within 4 percentage points of the truth about the population 95% of the time.

• if Gallup takes another poll on this issue, the results of the second poll will lie between 71% and 79%.

• there is convincing evidence that more than 79% of all US adults would vote for term limits.

• Gallup can be 95% confident that between 71% and 79% of the adults in the sample would vote for term limits.

A political poll was conducted by calling land-line telephones. The researchers conducting the poll are concerned about the possibility of undercoverage because some people do not own a phone or own only a cell phone. Which of the following is the best way for them to correct for this source of bias?

• Use a lower confidence level, such as 90%.

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

• Select a larger sample.

• Throw this sample out and start over again with a better sampling method.

A 95% confidence interval for p, the proportion of all shoppers at a large grocery store who purchase cookies, is 0.236 to 0.282. The point estimate and margin of error for this interval are:

• point estimate = 0.236; margin of error = 0.282

• point estimate = 0.236; margin of error = 0.046

• point estimate = 0.259; margin of error = 0.046

• point estimate = 0.259; margin of error = 0.023

A quality control manager at a manufacturing plant wants to estimate the mean length of metal rods produced by a certain machine. The manager is deciding between a 95% confidence level and a 99% confidence level. Compared to a 95% CI, a 99% CI will be

• narrower and would involve a larger risk of being incorrect.

• wider and would involve a smaller risk of being incorrect.

• narrower and would involve a smaller risk of being incorrect.

• wider and would involve a larger risk of being incorrect.

A quality control manager at a manufacturing plant wants to estimate the mean length of metal rods produced by a certain machine. The researcher is deciding between a sample of size n = 500 and a sample of size n = 1000. Compared to suing a sample size of n = 500, a 95% CI based on a sample size of n = 1000 will be

• narrower and would involve a larger risk of being incorrect.

• narrower and would involve a smaller risk of being incorrect.

• narrower and would involve the same risk of being incorrect.

• wider and would involve a smaller risk of being incorrect.

Isabel selects a simple random sample of 28 seniors at her school and finds that 20 of them are planning to participate in the school's annual capture-the-flag game. She wants to construct a CI for p = the proportion of all seniors who plan to participate in the game, but she realizes she hasn't met all the conditions for constructing the interval. Which condition for this procedure has she failed to meet?

• n ≥ 30

• np̂ ≥ 10

• n(1 - p̂) ≥ 10

• The population must be approximately normal.

Most people can roll their tongues, but some can't. Suppose we are interesting in determining what proportion of people in a certain population can roll their tongues. We test a random sample of 80 people from this population and find that 64 can roll their tongues. The margin of error for a 95%CI for the true proportion of tongue rollers in this population is closest to

• 0.004

• 0.045

• 0.088

• 0.176

Many TV viewers express doubts about the validity of certain commercials. In an attempt to answer their critics, Times Group USA wishes to estimate the proportion of consumers who believe what is shown in Timex TV commercials. Let p represent the true proportion of consumers who believe what is shown in Timex TV commercials. Which of the following is the smallest number of consumers that Timex can survey to guarantee a margin of error of 0.05 or less at the 99% confidence level?

• 600

• 650

• 700

• 750

In checking conditions for constructing CIs for a population mean, it's important to plot the distribution of sample data. Each dotplot shoss the distribution of a sample from a different population. For which of the three samples would it be safe to construct a one-sample t interval for the population mean?

• Sample X only

• Sample Y only

• Sample Y and Z

• None of the samples

You want to calculate a 98% CI for a population mean from a sample of size n = 18. What is the appropriate critical value t*?

• 2.110

• 2.224

• 2.552

• 2.567