Question

n a survey of 700 year 2005 high school graduates, it was found that 50.3% had enrolled in colleges, 11.1% in vocational institutions, while the other 38.6% did not pursue any further studies. Perform a test of hypotheses to determine whether the college enrollment rate in the population of year 2005 high school graduates was significantly higher than 48%. (Calculate the P-value.) Round to four decimal places.

Answer 1

`z=\frac{0.503-0.48}{\sqrt{(0.48(1-0.48))/(700)}}=1.218`

Now we can calculate the p value given by:

`p_v =P(z>1.218)=0.1116`

Explanation:

Information provided

n=700 represent the random sample selected

`\hat p=0.503` estimated proportion of college enrollment

`p_o=0.48` is the value that we want to test

z would represent the statistic

`p_v` represent the p value (variable of interest)

System of hypothesis

we want to check if the true proportion for the college enrollment is higher thna 0.48, the system of hypothesis are:

Null hypothesis:
`p\leq 0.48`

Alternative hypothesis:
`p > 0.48`

The statistic is given by:

`z=\frac{\hat p -p_o}{\sqrt{(p_o (1-p_o))/(n)}}` (1)

Replacing the info given we have:

`z=\frac{0.503-0.48}{\sqrt{(0.48(1-0.48))/(700)}}=1.218`

Now we can calculate the p value given by:

`p_v =P(z>1.218)=0.1116`