Samples and Margin of Error

Construct a 90% confidence interval of a random sample size of 19 cows with a mean of 155.526 and a standard deviation of 19.993. 

• (146.54, 164.52)

• (147.57, 163.48)

• (147.59, 163.46)

• (143.69, 167.36)

In a recent poll of 803 randomly selected baseball fans in Connecticut, 44% said their favorite team was the Yankees. If researchers wanted to reduce the margin of error to at most 2%, how many baseball fans do they have to randomly select? 

• 1564

• 2367

• 803

• 3170

The Gallup Poll interviews 1600 people. Of these,18% say that they jog regularly. The news report adds: “The poll had a margin of error of plus or minus three percentage points at a 95% confidence level.”

You can safely conclude that

• 95% of all Gallup Poll samples like this one give answers within ±3% of the true population value.

• if Gallup took many samples, 95% of them would find that 18% of the people in the sample jog.

• the percent of the population who jog is certain to be between 15% and 21%.

• 95% of the population jog between 15% and 21% of the time.

• we can be 95% confident that the sample proportion is captured by the confidence interval.

A confidence interval for a difference in proportions is −0.077 to 0.013. What are the point estimate and the margin of error for this interval?

• –0.032, 0.045

• –0.032, 0.090

• –0.032, 0.180

• –0.045, 0.032

• –0.045, 0.090

In a random sample of 100 students from a large high school, 37 regularly bring a reusable water bottle from home. Which of the following gives the correct value and interpretation of the standard error of the sample proportion?

• In samples of size 100 from this school, the sample proportion of students who bring a reusable water bottle from home will be at most 0.095 from the true proportion.

• In samples of size 100 from this school, the sample proportion of students who bring a reusable water bottle from home will be at most 0.048 from the true proportion.

• In samples of size 100 from this school, the sample proportion of students who bring a reusable water bottle from home typically varies by about 0.095 from the true proportion.

• In samples of size 100 from this school, the sample proportion of students who bring a reusable water bottle from home typically varies by about 0.048 from the true proportion.

• There is not enough information to calculate the standard error.

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

A marketing assistant for a technology firm plans to randomly select 1000 customers to estimate the proportion who are satisfied with the firm’s performance. Based on the results of the survey, the assistant will construct a 95% confidence interval for the proportion of all customers who are satisfied. The marketing manager, however, says that the firm can afford to survey only 250 customers. How will this decrease in sample size affect the margin of error?

• The margin of error will be about 4 times larger.

• The margin of error will be about 2 times larger.

• The margin of error will be about the same size.

• The margin of error will be about half as large.

• The margin of error will be about one-fourth as large.

A telephone poll of an SRS of 1234 adults found that 62% are generally satisfied with their lives. The announced margin of error for the poll was 3%. Does the margin of error account for the fact that some adults do not have telephones?

• Yes; the margin of error accounts for all sources of error in the poll.

• Yes; taking an SRS eliminates any possible bias in estimating the population proportion.

• Yes; the margin of error accounts for undercoverage but not nonresponse.

• No; the margin of error accounts for nonresponse but not undercoverage.

• No; the margin of error only accounts for sampling variability.

A sample of 30 women finds the mean height to be 62.3 in and the standard deviation to be 1.5 in. Find the margin of error of women's heights with a 95% CL.

• 699

• 0.56

• 0.537

• 19.325

A 90% confidence interval for the mean speed driven by cars on East Main St. is given by (21, 45). What was the margin of error of this study?

• 12

• 24

• 33

• None of these.