Update 09-hypothesis-testing.Rmd

Author: ismayc

09-hypothesis-testing.Rmd

@@ -742,7 +742,7 @@ prop_metal_popular <- round(prop_metal_popular, 3)
 prop_deephouse_popular <- round(prop_deephouse_popular, 3)
 ```
 
-So in this one sample of a hypothetical universe of no difference in genre popularity, $`r n_metal_popular`/26 = `r prop_metal_popular` = `r prop_metal_popular*100`\%$ of metal songs were popular. On the other hand, $`r n_deephouse_popular`/26 = `r prop_deephouse_popular` = `r prop_deephouse_popular*100`\%$ of deep house songs were popular. Let's next compare these two values. It appears that metal tracks were popular at a rate that was $`r prop_metal_popular ` - `r prop_deephouse_popular ` = `r diff_prop` = `r diff_prop*100`\$ percentage points different than deep house songs.
+So in this one sample of a hypothetical universe of no difference in genre popularity, $`r n_metal_popular`/26 = `r prop_metal_popular` = `r prop_metal_popular*100`\%$ of metal songs were popular. On the other hand, $`r n_deephouse_popular`/26 = `r prop_deephouse_popular` = `r prop_deephouse_popular*100`\%$ of deep house songs were popular. Let's next compare these two values. It appears that metal tracks were popular at a rate that was $`r prop_metal_popular ` - `r prop_deephouse_popular ` = `r diff_prop` = `r diff_prop*100`$ percentage points different than deep house songs.
 
 Observe how this difference in rates is not the same as the difference in rates of `r observed_test_statistic` = `r observed_test_statistic*100`% we originally observed. This is once again due to *sampling variation*. How can we better understand the effect of this sampling variation? By repeating this shuffling several times!
 
@@ -788,7 +788,7 @@ sampling_scenarios |>
 
 So, based on our sample of $n_m = 1000$ metal tracks and $n_f = 1000$ deep house tracks, the *point estimate* for $p_{m} - p_{d}$ is the *difference in sample proportions*
 
-$$\widehat{p}_{m} -\widehat{p}_{f} = `r p_metal_popular` - `r p_deephouse_popular` = `r observed_test_statistic`$$. 
+$$\widehat{p}_{m} -\widehat{p}_{f} = `r p_metal_popular` - `r p_deephouse_popular` = `r observed_test_statistic`.$$ 
 
 This difference in favor of metal songs of `r observed_test_statistic` (`r observed_test_statistic*100` percentage points) is greater than 0, suggesting metal songs are more popular than deep house songs.