Answer
a. $H_{o}: p = 0.105$
$H_{1}: p > 0.105$
b. Type-I Error: Sample evidence leads sociologist to believe that the proportion of births to teenage mothers has increased. However, in fact it has not increased.
c. Type-II Error: Sample evidence leads sociologist to believe that the proportion of births to teenage mothers has not increased. However, in fact it did increase.
Work Step by Step
a. The null hypothesis (no change in registered births to teenage mothers):
$H_{o}: p = 0.105$
Alternative hypothesis (the number of registered births has increased):
$H_{1}: p > 0.105$
b. Type-I Error: Sample evidence leads sociologist to believe that the proportion of births to teenage mothers has increased. However, in fact it has not increased. In other words, the scientists have rejected the null hypothesis ($H_o$), but it in fact is true.
c. Type-II Error: Sample evidence leads sociologist to believe that the proportion of births to teenage mothers has not increased. However, in fact it did increase. In other words, the scientists have not rejected the null hypothesis ($H_o$), when in fact the alternative hypothesis ($H_1$) is true.
