Confidence Intervals

Which z-value is used for a 95% confidence interval?

• 2.58

• 1.66

• 1.96

• 2.33

Margin of Error is equal to:

• Standard Deviation

• 2 * Standard Deviation

• Critical Value

• Point Estimate

Which of the following changes to a study would result in a smaller confidence interval?

• increasing the confidence level, increasing the sample size

• increasing the confidence level, decreasing the sample size

• decreasing the confidence level, decreasing the sample size

• decreasing the confidence level, increasing the sample size.

A research company wants to estimate the proportion of people who like oatmeal. They want the confidence level to be 95%. The company gets 325 people to sign up for the survey, but on the day that the survey is issued, only 250 people show up and take the survey. What happens to the confidence interval?

• It stays the same

• It gets smaller

• It gets larger

• Not enough information

A statistician proposed a new method for constructing a 90 percent confidence interval to estimate the median of assessed home values for homes in a large community. To test the method, the statistician will conduct a simulation by selecting 10,000 random samples of the same size from the population. For each sample, a confidence interval will be constructed using the new method. If the confidence level associated with the new method is actually 90 percent, which of the following will be captured by approximately 9,000 of the confidence intervals constructed from the simulation?

• The sample mean

• The sample median

• The sample standard deviation

• The population mean

• The population median

A polling agency conducted a survey by selecting 100 random samples, each consisting of 1,200 United States citizens. The citizens in each sample were asked whether they were optimistic about the economy. For each sample, the polling agency created a 95 percent confidence interval for the proportion of all United States citizens who were optimistic about the economy. Which of the following statements is the best interpretation of the 95 percent confidence level?

• With 100 confidence intervals, we can be 95% confident that the sample proportion of citizens of the United States who are optimistic about the economy is correct.

• We would expect about 95 of the 100 confidence intervals to contain the proportion of all citizens of the United States who are optimistic about the economy.

• We would expect about 5 of the 100 confidence intervals to not contain the sample proportion of citizens of the United States who are optimistic about the economy.

• Of the 100 confidence intervals, 95 of the intervals will be identical because they were constructed from samples of the same size of 1,200.

• The probability is 0.95 that 100 confidence intervals will yield the same information about the sample proportion of citizens of the United States who are optimistic about the economy

A commercial for a breakfast cereal is shown during a certain television program. The manufacturer of the cereal wants to estimate the percent of television viewers who watch the program. The manufacturer wants the estimate to have a margin of error of at most 0.02 at a level of 95 percent confidence. Of the following, which is the smallest sample size that will satisfy the manufacturer’s requirements?

• 40

• 50

• 100

• 1700

• 2500

Meteorologists are interested in the relationship between minimum pressure and maximum wind speed of hurricanes. The minimum pressure, in millibars, and maximum wind speed, in knots, were collected for a random sample of 100 hurricanes from the year 1995 to the year 2012. A regression analysis of maximum wind speed on minimum wind pressure produced a 95 percent confidence interval of (-1.42, -1.20) for the slope of the least-squares regression line. Which statement is a correct interpretation of the interval?

• The probability is 0.95 that wind speed will decrease, on average, between 1.20 knots and 1.42 knots for each millibar increase in minimum pressure.

• The probability is 0.95 that a different sample of 100 hurricanes will result in an increase, on average, of wind speed between 1.20 knots and 1.42 knots for each millibar increase in minimum pressure.

• We can be 95% confident that wind speed decreases, on average, between 1.20 knots and 1.42 knots for each millibar increase in minimum pressure.

• We can be 95% confident that wind speed increases, on average, between 1.20 knots and 1.42 knots for each millibar increase in minimum pressure.

• We can be 95% confident that, for any sample of hurricanes, the wind speed will decrease, on average, between 1.20 knots and 1.42 knots for each millibar increase in minimum pressure.

The management team of a company with 10,000 employees is considering installing charging stations for electric cars in the company parking lots. In a random sample of 500 employees, 15 reported owning an electric car. Which of the following is a 99 percent confidence interval for the proportion of all employees at the company who own an electric car?

• 
• 
• 
• 
• 

On the day before an election in a large city, each person in a random sample of 1,000 likely voters is asked which candidate he or she plans to vote for. Of the people in the sample, 55 percent say they will vote for candidate Taylor. A margin of error of 3 percentage points is calculated. Which of the following statements is appropriate?

• The proportion of all likely voters who plan to vote for candidate Taylor must be the same as the proportion of voters in the sample who plan to vote for candidate Taylor (55 percent), because the data were collected from a random sample.

• The sample proportion minus the margin of error is greater than 0.50, which provides evidence that more than half of all likely voters plan to vote for candidate Taylor.

• It is not possible to draw any conclusion about the proportion of all likely voters who plan to vote for candidate Taylor because the 1,000 likely voters in the sample represent only a small fraction of all likely voters in a large city.

• It is not possible to draw any conclusion about the proportion of all likely voters who plan to vote for candidate Taylor because this is not an experiment.

• It is not possible to draw any conclusion about the proportion of all likely voters who plan to vote for candidate Taylor because this is a random sample and not a census.