Question

1. A group of doctors is deciding whether or not to perform an operation. Suppose the null hypothesis, H₀, is: the surgical procedure will go well. State the Type I and Type II errors in complete sentences, and explain which is the error with the greater consequence and why.

2.

An article posted on your college's website claims that 12% of the students at the school use marijuana. You randomly sample 140 students, and 12 students reply that they do indeed use marijuana. You want to conduct a hypothesis test at a 5% level of significance.

What should your conclusion be?

		You can reject the claim made in the article, since the p-value is less than 0.05. The proportion of students that use marijuana is likely less than 12%.
		You can not reject the claim made in the article, since the p-value is greater 0.05. The claim that 12% of students use marijuana should be considered accurate.
		You can not reject the claim made in the article, since the p-value is greater 0.05. There is not sufficient evidence in the sample to dispute the claim that 12% of students use marijuana.
		You can reject the claim made in the article, since the p-value is less than 0.05. The proportion of students that use marijuana is likely greater than 12%.

Answer 1

1.
Type 1 error is possible only when it reject the null hypothesis
Type 2 error is possible only when it fails reject the null hypothesis
2.
Given that,
possibile chances (x)=12
sample size(n)=140
success rate ( p )= x/n = 0.086
success probability,( po )=0.12
failure probability,( qo) = 0.88
null, Ho:p=0.12
alternate, H1: p!=0.12
level of significance, α = 0.05
from standard normal table, two tailed z α/2 =1.96
since our test is two-tailed
reject Ho, if zo < -1.96 OR if zo > 1.96
we use test statistic z proportion = p-po/sqrt(poqo/n)
zo=0.08571-0.12/(sqrt(0.1056)/140)
zo =-1.248
| zo | =1.248
critical value
the value of |z α| at los 0.05% is 1.96
we got |zo| =1.248 & | z α | =1.96
make decision
hence value of |zo | < | z α | and here we do not reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != -1.24838 ) = 0.21189
hence value of p0.05 < 0.2119,here we do not reject Ho
ANSWERS
---------------
null, Ho:p=0.12
alternate, H1: p!=0.12
test statistic: -1.248
critical value: -1.96 , 1.96
decision: do not reject Ho
p-value: 0.21189
p value is greater than alpha value
we do not have enough evidence to support the claim that 12% of the students at the school use marijuana.