Merge pull request #506 from e-clin/patch-9

Update 08-confidence-intervals.Rmd

08-confidence-intervals.Rmd

@@ -36,7 +36,7 @@ p_red <- bowl %>%
 n_balls_sample <- 50L
 ```
 
-In Chapter \@ref(sampling), we studied sampling. We started with a "tactile" exercise where we wanted to know the proportion of balls in the sampling bowl in Figure \@ref(fig:sampling-exercise-1) that are red. While we could have performed an exhaustive count, this would have been a tedious process. So instead, we used a shovel to extract a sample of `r n_balls_sample` balls and used the resulting proportion that were red as an *estimate*. Furthermore, we made sure to mix the bowl's contents before every use of the shovel. Because of the randomness created by the mixing, different uses of the shovel yielded different proportions red and hence different estimates of the proportion of the bowl's balls that are red. 
+In Chapter \@ref(sampling), we studied sampling. We started with a "tactile" exercise where we wanted to know the proportion of balls in the sampling bowl in Figure \@ref(fig:sampling-exercise-1) that are red. While we could have performed an exhaustive count, this would have been a tedious process. So instead, we used a shovel to extract a sample of `r n_balls_sample` balls and used the resulting proportion that were red as an *estimate*. Furthermore, we made sure to mix the bowl's contents before every use of the shovel. Because of the randomness created by the mixing, different uses of the shovel yielded different proportions of red and hence different estimates of the proportion of the bowl's balls that are red. 
 
 ```{r echo=FALSE, purl=FALSE}
 # This code is used for dynamic non-static in-line text output purposes
@@ -967,7 +967,7 @@ So in our case, 95% of values of the bootstrap distribution will lie within $\pm
 
 $$\overline{x} \pm `r qnorm(0.975) %>% round(2)` \cdot SE = (\overline{x} - `r qnorm(0.975) %>% round(2)` \cdot SE, \, \overline{x} + `r qnorm(0.975) %>% round(2)` \cdot SE).$$
 
-Computation of the 95% confidence interval can once again be done by piping the `bootstrap_distribution` data frame we created into the `get_confidence_interval()` function. However, this time we set the first `type` argument to be `"se"`. Second, we must specify the `point_estimate` argument in order to set the center of the confidence interval. We set this to be the sample mean of the original sample of `r num_pennies` pennies of `r x_bar_point <- x_bar %>% pull(mean_year) %>% round(2); x_bar_point` we saved in `x_bar` earlier.
+Computation of the 95% confidence interval can once again be done by piping the `bootstrap_distribution` data frame we created into the `get_confidence_interval()` function. However, this time we first set the `type` argument to be `"se"`. Second, we must specify the `point_estimate` argument in order to set the center of the confidence interval. We set this to be the sample mean of the original sample of `r num_pennies` pennies of `r x_bar_point <- x_bar %>% pull(mean_year) %>% round(2); x_bar_point` we saved in `x_bar` earlier.
 
 ```{r}
 standard_error_ci <- bootstrap_distribution %>%