MAT 152 Test 6 Review: Confidence Intervals

True or False: A larger sample size produces a longer confidence interval for the population mean.

• True

• False

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

• True

• False

Tags

CCSS.HSS.IC.B.4

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

The point estimate for the population mean of an x distribution is x-bar, computed from a random sample of the x distribution.

• True

• False

Tags

CCSS.6.SP.A.3

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

Tags

CCSS.HSS.IC.B.4

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

Tags

CCSS.HSS.ID.A.4

Allen's hummingbird has been studied by zoologist Bill Alther. A small group of 15 Allen's hummingbirds has been under study in Arizona. The average weight for these birds is 3.15 grams. Based on previous studies, we can assume that the weights of Allen's hummingbirds have a normal distribution with a standard deviation of 0.33 gram.

Find an 80% confidence interval for the average weights of Allen's hummingbirds in the study region.

• (3 g, 4 g)

• (3.04 g, 3.26 g)

• (2.82 g, 3.26 g)

• (2.28 g, 2.36 g)

Tags

CCSS.HSS.IC.B.4

Allen's hummingbird has been studied by zoologist Bill Alther. A small group of 15 Allen's hummingbirds has been under study in Arizona. The average weight for these birds is 3.15 grams. Based on previous studies, we can assume that the weights of Allen's hummingbirds have a normal distribution with a standard deviation of 0.33 gram.

Find the sample size necessary for an 80% confidence level with a maximal margin of error E=0.08 for the mean weights of the hummingbirds.

• 26

• 27

• 28

• 29

Tags

CCSS.HSS.IC.B.4

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

Tags

CCSS.HSS.IC.B.4