Confidence Interval for a Mean, Sigma Known

If the original x distribution has a relatively small standard deviation, the confidence interval for the population mean will be relatively short.

• True

• False

For the same random sample, when the confidence level c is reduced, the confidence interval for the mean becomes shorter.

• True

• False

The value z_c is a value from the standard normal distribution such that P(-z_c<x<z_c)=c.

• True

• False

Consider a random sample of size n from an x distribution. For such a sample, the margin of error for estimating the population mean is the magnitude of the difference between x-bar and mu.

• True

• False

Suppose x has a mound-shaped distribution with sigma=9. A random sample of size 36 has sample mean 20. Is it appropriate to use a normal distribution to compute the confidence interval?

• Yes

• No

Overproduction of uric acid in the body can be an indication of cell breakdown. This may be an advance indication of illness such as gout, leukemia, or lymphoma. Over a period of months, an adult male patient has taken eight blood tests for uric acid, which had the mean concentration of 5.3 mg/dl. The distribution of uric acid in healthy adult males can be assumed to be normal with a standard deviation of 1.85 mg/dl. The level of confidence sis 95%. What is the margin of error E?

• 4.07 mg/dl

• 1.82 mg/dl

• 1.48 mg/dl

• 1.28 mg/dl

Suppose an archaeologist discovers seven fossil skeletons from a previously unknown species of miniature horse. Reconstructions of the skeletons of these seven miniature horses show the shoulder heights (in centimeters) to be 45.3, 47.1, 44.2, 46.8, 46.5, 45.5, 47.6 Assume that the population of shoulder heights is approximately normal. Find the 99% confidence interval for the mean of the shoulder heights of the entire population of such horses.

• (45.4 cm, 48.7 cm)

• (46 cm, 48 cm)

• (45 cm, 48 cm)

• (44.5 cm, 47.8 cm)

When all other quantities remain the same, how does increasing the level of confidence affect the width of a confidence interval?

• nothing changes

• CI width increases

• CI width decreases

When all other quantities remain the same, how does increasing the sample size affect the width of a confidence interval?

• nothing changes

• CI width increases

• CI width decreases

When all other quantities remain the same, how does increasing the population standard deviation affect the width of a confidence interval?

• nothing changes

• CI width increases

• CI width decreases