SOLUTION: Achaiah made a claim that at least 5% of the college male students drives racing car. His friend Sofia finds this hard to believe and decided to check the validity of Achaiah's cla
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-> SOLUTION: Achaiah made a claim that at least 5% of the college male students drives racing car. His friend Sofia finds this hard to believe and decided to check the validity of Achaiah's cla
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Question 1202069: Achaiah made a claim that at least 5% of the college male students drives racing car. His friend Sofia finds this hard to believe and decided to check the validity of Achaiah's claim, so she took a random sample. At 0.05, does Sofia have sufficient evidence to reject Achaiah's claim if there were 19 racing car in her sample of 750 cars? Answer by math_tutor2020(3816) (Show Source):
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:
Alternate:
The claim "at least 5% of the college male students drive a racing car" is in the null.
Technically the null should be , but I'll go with 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 https://www.ztable.net/
Similar tables are found in the back of your stats textbook.
Alternatively you could use a stats calculator like this one https://davidmlane.com/normal.html
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 must be the case.
Answer: Sofia has sufficient evidence to reject Achaiah's claim
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