Confidence Interval for a Mean, Sigma Known

A confidence interval is centered around...

• a parameter

• a statistic

• the sample size

• the population size

A sample of size 49 has sample mean 35 and sample standard deviation 11. Construct a 98% confidence interval for the population mean using this information.

• 13.34,38.66

• 38.66,31.34

• 31.34,38.66

• 38.66,13.34

A random sample is drawn from a population of known standard deviation 11.3. Construct a 90% confidence interval for the population mean based on the information given (not all of the information given need be used)

n= 100, x¯ = 105.2, s = 11.2

• 103.35,107.05

• 93.35,117.05

• 107.05,103.35

• 117.05,93.35

Find the number

z

needed in the construction of a confidence interval:

when the level of confidence is 90%

• 1.64

• 2.58

• 2.33

• 1.96

Find the number

z​​

needed in the construction of a confidence interval:

when the level of confidence is 99%

• 1.64

• 1.96

• 2.33

• 2.58

A random sample of 120 students from a large university yields mean GPA 2.71 with sample standard deviation 0.51. Construct a 90% confidence interval for the mean GPA of all students at the university

• 1.63,3.79

• 2.63,2.79

• 3.79,1.63

• 2.97,2.63

Find the minimum sample size necessary to construct a 99% confidence interval for mu with a margin of error E=0.2. Assume that the population standard deviation is sigma=1.3.

• 208

• 280

• 260

• 206

An economist wishes to estimate, with a 95% confidence interval, the yearly income of welders with at least five years experience to within $1,000. He estimates that the range of incomes is no more than $24,000, so using the Empirical Rule he estimates the population standard deviation to be about one-sixth as much, or about $4,000. Find the estimated minimum sample size required.

• 14

• 41

• 16

• 61

Random samples of size 225 are drawn from a population with mean 100 and standard deviation 20. Find the mean and standard deviation of the sample mean

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)