Question

In the pbkid data set there were 124 children and 23 of them had colic. Using the information from the pbkid data test if the prevalence of colic differs from that in the general public, which is 7%.

Answer 1

Null hypothesis:- The prevalence of colic not differs from that in the general public

so, Alternate hypothesis :- The prevalence of colic differs from that in the general public

we have po = 0.07 and p' = 23/124 = 0.19

and n =124

Using the formula

z = $(p' - po)/\sqrt{po*(1-po)/n}$

setting the given values, we get

z = $(0.19-0.07)/\sqrt{0.07*(1-0.07)/124}$

So, the test statistic is z = 5.24

P value corresponding to z value of 5.24 for a two-tailed hypothesis is 0.0000 at 0.05 significance level

so, the p value < 0.05, this means p value is significant and we can reject the null hypothesis.

Thus, we can conclude that the prevalence of colic differs from that in the general public