SOLUTION: I am having trouble with calculating p-values. I have two problems that I just can't figure out. This is the first: A survey of 120 high school students shows that 39 of them wo

Question 67802This question is from textbook Statistics Principles and Methods
: I am having trouble with calculating p-values. I have two problems that I just can't figure out. This is the first:
A survey of 120 high school students shows that 39 of them work over 20 hours per week during the school year. Does it demonstrate the conjecture that more than 25% of the high school students work over 20 hours per week during the school year? (Answer by calculating the P-value.)
I started out calculating the sample proportion:
p^ = x / n = 39/120 = 0.325
which means that 32.5 % work more than 20 hrs. per week, which is more than 25%, but how do you show that by calculating the P-value? I tried to figure out the test statistic, but got lost. Thanks for any help you can give.
This question is from textbook Statistics Principles and Methods

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A survey of 120 high school students shows that 39 of them work over 20 hours per week during the school year. Does it demonstrate the conjecture that more than 25% of the high school students work over 20 hours per week during the school year? (Answer by calculating the P-value.)
I started out calculating the sample proportion:
p^ = x / n = 39/120 = 0.325
which means that 32.5 % work more than 20 hrs. per week, which is more than 25%, but how do you show that by calculating the P-value? I tried to figure out the test statistic, but got lost. Thanks for any help you can give.
--------------------
Ho:p=0.25
Ha:p>0.25
--------------
You figured p-hat=0.325
The test statistic is the following z-value.
z(0.325)=(0.325-0.25)/sqrt[(0.325*0.675)/120]
=0.075/0.042756=1.7541
Draw a normal curve; label the horizontal axis as "z";
mark "0" as the mean; put a point at 1.7541;
Calculate the amount of area to the right of 1.7541 as
0.0397066
This is the p-value you are looking for.
This p-value means there is approximately a 4% chance
that the test proportion (0.325) could be higher than
the proportion seen in the sample. That is quite low
and would result in rejecting Ho which said the population
proportion was 0.25. It probably is higher.
Hope this helps.
Cheers,
Stan H.

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