Find $z_{\alpha/2}$ for an $84\%$ confidence interval.
Find $z_{\alpha/2}$ for a $93\%$ confidence interval.
How many times should we flip a coin to get a $98\%$ confidence interval for the probability that the coin lands heads with margin of error at most .01?
How large a sample would you need in order to estimate within $2\%$ the probability of rolling a "six" on a 6-sided die with $90\%$ confidence? In a pilot study, the die was rolled 200 times and landed on "six" 79 times.
In a sample of 100 M&M's, 8 of them were brown. Find a $94\%$ confidence interval for the proportion of M&M's that are brown.
The coin lands heads 48 times out of 100 tosses. Find a $97\%$ confidence interval for the probability that the coin lands heads.
The American Automobile Association claims that $54\%$ of fatal car/truck accidents are caused by driver error. A researcher studies 35 randomly selected accidents and finds that 14 were caused by driver error. Find a $92\%$ confidence interval for the proportion of fatal car/truck accidents caused by driver error.
A survey showed that among 785 randomly selected subjects who completed four years of college, $18.3\%$ smoke. Find a $96\%$ confidence interval for the proportion of those with four years of college who smoke.
In a random sample of 250 children, it was found that 87 children were dressed as movie characters for Halloween. Find a $92\%$ confidence interval for the proportion of children who dress as movie characters for Halloween.
A $90\%$ confidence interval for the proportion of the population in favor of an issue is $.41 \lt p \lt .47$. Give the point estimate and the maximum error of the estimate.
For a random sample of students, a $95\%$ confidence interval for the proportion who prefer chocolate ice cream is $[0.31, 0.39]$. Find the point estimate and the margin of error.
Beth and Lori share a digital music player that has a feature that randomly selects which song to play. A total of 2345 songs were loaded onto the player, some by Beth and the rest by Lori. Suppose that when the player was in the random-selection mode, 36 of the first 50 songs selected were songs loaded by Beth.
Construct and interpret a $90\%$ confidence interval for the proportion of songs on the player that were loaded by Beth.
How large a sample would be needed to estimate the proportion of songs loaded by Beth with $99\%$ confidence and margin of error at most $5\%$?