Question

27. In constructing a confidence interval estimate of the population mean you decide to select 49 random observations to get your point estimate of the mean (sample mean). Your friend is also constructing a similar confidence interval estimate but decides to use a sample size of 36 random observations.
Which of the following is true?
a.) Your confidence interval estimate is narrower
b.) Your friend’s confidence interval estimate has a greater degree of confidence
c.) Your confidence interval estimate is wider
d.) Your confidence interval estimate has a greater degree of confidence
2.) The width of a confidence interval estimate for a proportion will be:
a.) Narrower for 99% confidence level than for a 95% confidence level
b.) Wider for a sample size of 100 than for a sample size of 75
c.) Narrower for 90% confidence level than for a 95% confidence level
d.) Narrower when the sample proportion is .50 than when the sample proportion is 20.

Answer 1

Answer:

1) a.) Your confidence interval estimate is narrower

2) c.) The width of a confidence interval estimate for a proportion will be narrower for 90% confidence level than for a 95% confidence level

Step-by-step explanation:

Confidence Interval can be stated as  M±ME where

• M is the sample mean

• ME is the margin of error

Margin of Error determines the range of the confidence interval around the mean.

Margin of error (ME) of the mean can be calculated using the formula

ME=$\frac{z*s}{\sqrt{N} }$ where

• z is the corresponding statistic in the given confidence level

• s is the standard deviation of the sample(or the population if it is known)

• N is the sample size

From the formula we can reach the following conclusions:

• As N increases, ME decreases.

• as confidence level increases, corresponding statistic increases, and thus margin of error increases.

Since your sample size (49) is bigger than your friend's (36), your confidence interval is narrower, because margin of error is narrower.

Since the confidence level 90% has smaller statistic than the confidence level 95%, its confidence interval is narrower.

That is, we can estimate narrower confidence intervals with less confidence.