1. (8 Points) In order to estimate the proportion of residents in a town who drive alternative-fuel cars (e.g., electric, hybrid, or natural gas), a person records the number of cars passing through a certain intersection for a one-half hour time period. A total of 125 cars passed through the intersection at this time, where 14 were alternative-fuel vehicles. Find the 95% Wald, Agresti-Coull, Wilson, and Clopper-Pearson intervals using the given data. Interpret the intervals in the context of the experiment. Modify CIpi.R to find the intervals.

95% Intervals	Lower Limit	Upper Limit
Wald
Agresti-Coull
Wilson
Clopper-Pearson

95% Wald Interval

We would expect 95% of all similarly constructed intervals (repeat the sampling process and use the same type of interval) to contain the true alternative-fuel rate.

Alternatively, with 95% confidence, the true alternative-fuel rate is between _______ and _______.

95% Agresti-Coull Interval

We would expect 95% of all similarly constructed intervals (repeat the sampling process and use the same type of interval) to contain the true alternative-fuel rate.

Alternatively, with 95% confidence, the true alternative-fuel rate is between _______ and _______.

95% Wilson Interval

We would expect 95% of all similarly constructed intervals (repeat the sampling process and use the same type of interval) to contain the true alternative-fuel rate.

Alternatively, with 95% confidence, the true alternative-fuel rate is between _______ and _______.

95% Clopper-Pearson Interval

We would expect 95% of all similarly constructed intervals (repeat the sampling process and use the same type of interval) to contain the true alternative-fuel rate.

Alternatively, with 95% confidence, the true alternative-fuel rate is between _______ and _______.

2. (4 Points) Use the binom.confint() function from the binom package (demonstrated in CIpi.R) to confirm the intervals in #1.

95% Intervals	Lower Limit	Upper Limit
Wald
Agresti-Coull
Wilson
Clopper-Pearson

3. (6 Points) On pages 4 and 5 of the Better-Performing Confidence Intervals notes, the estimated true confidence level for a 95% Wald Confidence Interval when is found to be 0.898. Find the estimated true confidence level for a 95% Wald Confidence Interval when Simulate 1,000 samples using the rbinom( ) function with and Use a seed value of 4516.

The estimated true confidence level is _______.

4. (6 Points) On pages 6 and 7 of the Better-Performing Confidence Intervals notes, the true confidence level for a 95% Wald Confidence Interval when is found to be 0.9034437. Find the true confidence level for a 95% Wald Confidence Interval when

The true confidence level is ______.

5. (4 Points) In most billiards games, the person who breaks a rack of balls gets another turn if at least one ball is sunk, excluding the cue ball. This is advantageous for this person because there are a fixed number of balls that need to be sunk in order to win a game. In order to estimate one persons probability of success of sinking a ball on the break, there were 25 consecutive breaks performed in 8-ball billiards. Out of these 25, 15 breaks had a ball sunk. Find the 95% Clopper-Pearson confidence interval using the given data. Use R code similar to that on page 8 of the Better-Performing Confidence Intervals notes (with the qbeta function) to find the interval. Interpret the interval in the context of the experiment.

With 95% confidence, the true success rate is between _______ and ________.

We would expect _____% of all similarly constructed intervals (repeat the sampling process and use the same type of interval) to contain the true success rate of sinking a ball on the break.

6. (4 Points) Use the binom.confint( ) function from the binom package to confirm the interval in #5.

With 95% confidence, the true success rate is between _______ and ________.