Exam 8: Interval Estimation

The required sample size for the interval estimation of the population mean can be computed if we specify the population standard deviation σ, the value of z_α/2 based on the confidence level 100(1 − α)% and the desired margin of error D.

What is the minimum sample size required to estimate a population mean with 95% confidence when the desired margin of error is E = 1.5? The population standard deviation is known to be 10.75.

Students who graduated from college last year owed an average of $25,250 in student loans. An economist wants to determine if average debt has changed. She takes a sample of 40 recent graduates and finds that their average debt is $27,500 with a standard deviation of $9,120. Use 90% confidence interval. Which of the following conclusion is correct?

In an examination of purchasing patterns of shoppers, a sample of 16 shoppers revealed that they spent, on average, $54 per hour of shopping. Based on previous years, the population standard deviation is thought to be $21 per hour of shopping. Assuming that the amount spent per hour of shopping is normally distributed, find a 90% confidence interval for the mean amount.

What is t_α/2,df for a 95% confidence interval of the population mean based on a sample of 15 observations?

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

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?

An environmentalist is measuring the number of spotted leopard lizards in central California per acre. The environmentalist surveys six acres and finds signs of 24, 26, 30, 27, 28, and 27 lizards per acre. Construct a 95% confidence interval for the average number of leopard lizards per acre.

The confidence intervals for the population proportion are generally based on ________.

A researcher in campaign finance law wants to estimate the proportion of elementary, middle, and high school teachers who contributed to a candidate during a recent election cycle. 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 0.03 for a 95% confidence interval?

A machine that is programmed to package 1.20 pounds of cereal is being tested for its accuracy in a sample of 36 cereal boxes, the sample mean filling weight is calculated as 1.22 pounds. The population standard deviation is known to be 0.06 pounds. Which of the following conclusions is correct?

A 90% confidence interval is constructed for the population mean. If a 95% confidence interval had been constructed instead (everything else remaining the same), the width of the interval would have been ________ and the probability of making an error would have been ________.

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

A student interviewing at a major company wants to know his chances of getting a job offer. He surveyed 18 alumni that had interviewed with the company and found nine of them had received a job offer. Construct a 90% confidence interval for the population proportion.

What is z_α/2 for a 90% confidence interval of the population mean?

The height of high school basketball players is known to be normally distributed with a standard deviation of 1.75 inches. In a random sample of eight high school basketball players, the heights (in inches) are recorded as 75, 82, 68, 74, 78, 70, 77, and 76. Construct a 95% confidence interval on the average height of all high school basketball players.

Suppose taxi fares from Logan Airport to downtown Boston is known to be normally distributed and a sample of seven taxi fares produces a mean fare of $22.31 and a 95% confidence interval of [$20.5051, $24.2091]. Which of the following statements is a valid explanation of the confidence interval.

A company that produces computers recently tested the battery in its latest laptop in six separate trials. The battery lasted 8.23,7.89,8.14,8.25,8.30, and 7.95 hours before burning out in each of the tests. Assuming the battery duration is normally distributed, construct a 95% confidence interval for the mean battery life in the new model.

The daily revenue from the sale of fried dough at a local street vendor in Boston is known to be normally distributed with a known standard deviation of $120. The revenue on each of the last 25 days is noted, and the average is computed as $550. A 95% confidence interval is constructed for the population mean revenue. If the data from the last 40 days had been used, then the resulting 95% confidence intervals would have been ________.

If calculated required sample size is a noninteger value, we should always ________ calculated value.