Question

The Institute of Education Sciences measures the high school dropout rate as the percentage of 16- through 24-year-olds who are not enrolled in school and have not earned a high school credential. Last year, the high school dropout rate was 8.1%. A polling company recently took a survey of 1,000 people between the ages of 16 and 24 and found that 6.5% of them are high school dropouts. The polling company would like to determine whether the dropout rate has decreased. When testing whether the dropout rate has decreased, the appropriate hypotheses are

Answer 1

The appropriate hypothesis which is used to test the dropout rate are $H_{0}:p > =0.081$ and $H_{1}: p < 0.081$.

Given Drop out rate through 24 year old who are not enrolled is 8.1%, sample size=1000 and we have to find the hypothesis to test the drop out rate of the school.

The variable which needs to be studied is X=Number of individuals with age between 16 and 24 years old that are high school dropouts.

The parameter of interest is the proportion to high school drop outs is p.

Sample proportion=$p^{1}$=0.065

The hypothesis can be formed as under:

$H_{0}:p > =0.081$  (null hypothesis)

$H_{1}:p < 0.081$      ( alternate hypothesis)

Null hypothesis is a hypothesis which is tested for its validity and alternate hypothesis is hypothesis which is opposite of null hypothesis means if null hypothesis is rejected then the alternate hypothesis will be true.

$Z_{H_{0} }=(p^{1}-p)/\sqrt{p*(1-p)/n}$

=$0.065-0.081/\sqrt{(0.081*0.0919)/1000}$

=-1.85

Hence the appropriate hypothesis  are $H_{0}:p > =0.081$ and $H_{1}:p < 0.081$.

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