Estimating Mean When Sigma Is Known

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)

In the 3rd week of July, a random sample of 40 farming regions gave a sample mean of $6.88 per 100 pounds of watermelon. Assume the sigma is known to be $1.92 per 100 pounds. Find a 90% confidence interval for the population mean price (per 100 pounds) that farmers in this region get for their watermelon crop.

• ($6, $7)

• ($7.38, $6.38)

• ($6.38, $7.38)

• ($4.92, $8.80)

In the 3rd week of July, a random sample of 40 farming regions gave a sample mean of $6.88 per 100 pounds of watermelon. Assume the sigma is known to be $1.92 per 100 pounds. find the sample size necessary for a 90% confidence level with maximal margin of error E=0.3 for the mean price per 100 pounds of watermelon.

• 109

• 100

• 111

• 108

A company for a new process for manufacturing large artificial sapphires. In a trial run, 37 sapphires are produced. The distribution of weights is mound-shaped and symmetric. The mean weight for these 37 gems is 6.75 carats, and the sample standard deviation is 0.33 carat. Let mu be the mean weight for the distribution of all sapphires produced by the new process. The level of confidence is 95%. Find the margin of error E.

• 0.10 carat

• 0.11 carat

• 0.12 carat

• 0.14 carat

Which of these represents the confidence interval for the population mean with known sigma?

• a

• b

• c

• d

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

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

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

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