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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.

Respuesta :

Answer:

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

Now we can calculate the p value given by:

[tex]p_v =P(z>1.218)=0.1116[/tex]  

Step-by-step explanation:

Information provided

n=700 represent the random sample selected

[tex]\hat p=0.503[/tex] estimated proportion of college enrollment

[tex]p_o=0.48[/tex] is the value that we want to test

z would represent the statistic

[tex]p_v[/tex] 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:[tex]p\leq 0.48[/tex]  

Alternative hypothesis:[tex]p > 0.48[/tex]  

The statistic is given by:

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

Replacing the info given we have:

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

Now we can calculate the p value given by:

[tex]p_v =P(z>1.218)=0.1116[/tex]  

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