Exam 8: Interval Estimation

For a given confidence level 100(1 - α)% and population standard deviation σ, the width of the confidence interval for the population mean is wider, the smaller the sample size n.

How do the t_df and z distributions differ?

A large earthquake hit a city in South America. A survey of 2,000 houses found that 600 of them had collapsed. Construct a 95% confidence interval for the proportion of collapsed houses.

According to a report in USA Today, more and more parents are helping their young adult children get homes. Suppose eight persons in a random sample of 40 young adults who recently purchased a home in Kentucky received help from their parents. You have been asked to construct a 95% confidence interval for the population proportion of all young adults in Kentucky who received help from their parents. What is the margin of error for a 95% confidence interval for the population proportion?

A sample of the weights of 35 babies is taken from the local hospital maternity ward. The point estimate for the mean weight of the babies is 110.2 ounces with a sample standard deviation of 23.4 ounces. Construct a 90% confidence interval for the population mean baby weight at this hospital. Interpret this interval.

What is the purpose of calculating a confidence interval?

A Monster.com pool of 3,057 individuals asked, "What's the longest vacation you plan to take this summer?" The following relative frequency distribution summarizes the results. The 95% confidence interval for the proportion of people who plan a one-week vacation this summer is ________.

A medical devices company wants to know the number of hours its MRI machines are used per day. A previous study found a standard deviation of four hours. How many MRI machines must the company find data for in order to have a margin of error of at most 0.5 hour when calculating a 98% confidence interval?

Find the minimum sample size when we want to construct a 95% confidence interval on the population proportion for the support of candidate A in the following mayoral election. Candidate A is facing two opposing candidates. In a preselected poll of 100 residents, 22 supported candidate B and 14 supported candidate C. The desired margin of error is 0.06.

What conditions are required by the central limit theorem before a confidence interval of the population mean may be created?

The parameter p represents the ________ of successes in the population.

A string quartet in Maui wants to better understand its income stream, which primarily comes from playing at weddings. The cellist records the number of weddings the quartet plays in six successive months. Construct a 90% confidence interval from her results: 3, 5, 7, 4, 4, and 5.

According to a report in USA Today, more and more parents are helping their young adult children buy homes. You would like to construct a 90% confidence interval of the proportion of all young adults in Louisville, Kentucky, who received help from their parents in buying a home. How large a sample should you take so that the margin of error is no more than 0.06?

To estimate the mean earnings forecast for a large company, an investor looked up earnings forecasts from six financial analysts. The six forecasts he found were 200, 220, 300, 185, 210, and 210 (in millions). Suppose the investor knows the population standard deviation is 25 million. Calculate a 95% confidence interval of the population mean earnings forecast.

The sampling distribution of is based on a normal distribution on samples of any size.

Excel does not have a special function that allows to calculate t values.

What is t_α/2,df for a 99% confidence interval of the population mean based on a sample of 25 observations?

A sample of holiday shoppers is taken randomly from a local mall to determine the average daily spending on gifts. From a preselected sample, the standard deviation was determined to be $26. You would like to construct a 95% confidence interval for the mean daily spending on all holiday spending. A) Find the appropriate sample size necessary to achieve a margin of error of $5. B) Find the appropriate sample size necessary to achieve a margin of error of $8.

Suppose taxi fare from Logan Airport to downtown Boston is known to be normally distributed with a standard deviation of $2.50. The last seven times John has taken a taxi from Logan to downtown Boston, the fares have been $22.10, $23.25, $21.35, $24.50, $21.90, $20.75, and $22.65. What is a 95% confidence interval for the population mean taxi fare?

Which of the following is the correct formula for the margin of error in the interval estimation of p?