Exam 8: Interval Estimation

An analyst takes a random sample of 25 firms in the telecommunications industry and constructs a confidence interval for the mean return for the prior year. Holding all else constant, if he increased the sample size to 30 firms, how are the standard error of the mean and the width of the confidence interval affected?

Like the z distribution, the t_df distribution is symmetric around 0, bell-shaped, and with tails that approach the horizontal axis and eventually cross it.

If a small segment of the population is sampled then an estimate will be less precise.

A basketball coach wants to know how many free throws an NBA player shoots during the course of an average practice. The coach takes a random sample of 43 players and finds the average number of free throws shot per practice was 225 with a standard deviation of 35. Construct a 99% confidence interval for the average number of free throws in practice.

If a random sample of size n is taken from a normal population with a finite variance, then the statistic T = follows the t_df distribution with (n − 1) degrees of freedom, df.

A random sample of 130 mortgages in the state of Maryland was randomly selected. From this sample, 14 were found to be delinquent on their current payment. The 98% confidence interval for the proportion based on this sample is ________.

Statisticians like precision in their interval estimates. A low margin of error is needed to achieve this. Which of the following supports this when selecting sample sizes?

The starting salary of business students in a university is known to be normally distributed. A random sample of 18 business students results in a mean salary of $46,500 with a standard deviation of $10,200. Construct the 90% confidence interval for the mean starting salary of business students in this university.

A large city recently surveyed 1,354 streetlights, finding that 4.2% of them had burned out. Construct a 99% confidence interval for the proportion of the city's streetlights that are burned out.

A job candidate with an offer from a prominent investment bank wanted to estimate how many hours she would have to work per week during her first year at the bank. She took a sample of six first-year analysts, asking how many hours they worked in the last week. Construct a 95% confidence interval with her results: 64, 82, 74, 73, 78, and 87 hours.

A car dealership wants to estimate the percentage of customers who are satisfied with their customer service. Given that the car dealership has no prior knowledge of the proportion, how many customers would it have to sample to ensure a margin of error of no more than 5% for a 99% confidence interval?

A sample of 2,007 American adults was asked how they viewed China, with 17% of respondents calling the country "unfriendly" and 6% of respondents indicating the country was "an enemy." Construct a 95% confidence interval of the proportion of American adults who viewed China as either "unfriendly" or "an enemy."

In an examination of holiday spending (known to be normally distributed) of a sample of 16 holiday shoppers at a local mall, an average of $54 was spent per hour of shopping. Based on the current sample, the standard deviation is equal to $21. Find a 90% confidence interval for the population mean level of spending per hour.

When the required sample size calculated by using a formula is not a whole number, what is the best choice for the required sample size?

A politician wants to estimate the percentage of people who like his new slogan. Given that no prior estimate of the population proportion is available, what is the minimum sample size such that the margin of error is no more than 0.08 for a 95% confidence interval?

A sample of a given size is used to construct a 95% confidence interval for the population mean with a known population standard deviation. If a bigger sample had been used instead, then the 95% confidence interval would have been ________ and the probability of making an error would have been ________.

A large university is interested in the outcome of a course standardization process. They have taken a random sample of 100 student grades, across all instructors. The grades represent the proportion of problems answered correctly on a midterm exam. The sample proportion correct was calculated as 0.78. A) Construct a 90% confidence interval on the population proportion of correctly answered problems. B) Construct a 95% confidence interval on the population proportion of correctly answered problems.

For a given confidence level and population standard deviation, which of the following is true in the interval estimation of the population mean?

The minimum sample size n required to estimate a population mean with 95% confidence and the desired margin of error 1.5 was found to be 198. Which of the following is the approximate value of the assumed estimate of the population standard deviation?

A recent survey of 1,014 American adults found that 46% view environmental conditions as either "excellent" or "good" (Gallup, March 4-7). Construct a 95% confidence interval of the population proportion.