Exercise

# Sample proportion value effects on bootstrap CIs

One additional element that changes the width of the confidence interval is the sample parameter value, \(\hat{p}\).

Generally, when the true parameter is close to 0.5, the standard error of \(\hat{p}\) is larger than when the true parameter is closer to 0 or 1. When calculating a bootstrap t-confidence interval, the standard error controls the width of the CI, and here (given a true parameter of 0.8) the sample proportion is higher than in previous exercises, so the width of the confidence interval will be narrower.

Instructions

**100 XP**

`calc_p_hat()`

is shown in the script to calculate the sample proportions.`calc_t_conf_int()`

from the previous exercise has been updated to now use any value of`p_hat`

as an argument. Read their definitions and try to understand them.- Run the code to calculate the bootstrap t-confidence interval for the original population.
- Consider a new population where the true parameter is 0.8,
`one_poll_0.8`

. Calculate \(\hat{p}\) of this new sample, using the same technique as with the original dataset. Call it`p_hat_0.8`

. - Find the bootstrap t-confidence interval using the new bootstrapped data,
`one_poll_boot_0.8`

, and the new \(\hat{p}\).*Notice that it is narrower than previously calculated.*