Question 1202069
<font color=black size=3>
p = population proportion


n = sample size
phat = sample proportion
The job of phat is to estimate p.



In this problem we have
n = 750
phat = 19/750 = 0.025333 (approximate)
alpha = 0.05 = significance level


Now let's set up the two hypotheses
Null: {{{p >= 0.05}}}
Alternate: {{{p < 0.05}}}
The claim "at least 5% of the college male students drive a racing car" is in the null. 
Technically the null should be {{{p = 0.05}}}, but I'll go with {{{p >= 0.05}}} to match up with the phrasing from the claim.
The "less than" sign in the alternate hypothesis means we have a left tailed test.


The phat distribution will be centered at p = 0.05 and have standard error (SE) of...
SE = sqrt(p*(1-p)/n)
SE = sqrt(0.05*(1-0.05)/750)
SE = 0.0079582 which is approximate


Calculate the z score for the phat value of phat = 0.025333
z = (phat - p)/SE
z = (0.025333 - 0.05)/0.0079582
z = -3.09957
z = -3.10


Now use a table such as this one
<a href = "https://www.ztable.net/">https://www.ztable.net/</a>
Similar tables are found in the back of your stats textbook.
Alternatively you could use a stats calculator like this one
<a href = "https://davidmlane.com/normal.html">https://davidmlane.com/normal.html</a>
but I'll stick to the table route.


Use that table to see that
P(Z < -3.10) = 0.00097
This is the approximate area under the Z curve to the left of z = -3.10
Recall we're doing a left tailed test, so this area represents the p-value.


p-value = 0.00097
alpha = 0.05


The p-value is smaller than alpha, so we reject the null.
We conclude the alternate hypothesis {{{p < 0.05}}} must be the case.


Answer: Sofia has sufficient evidence to reject Achaiah's claim
</font>