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= 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 <em>narrower</em> confidence intervals with less confidence.