Answers - Millersville University

elieve that Jim Morrison (of The Doors) is still alive. The newspaper article began
with the claim that “almost 1 out of 10” students thinks that Jim Morrison is alive.
At the α = 0.025 significance level, test the claim that the true percentage is less than
10%.
(a) Identify the type I error for this test.
Type I error is made when we reject a true null hypothesis. The original claim
is that the proportion of students from the western US who believe Jim Morrison
is still alive is less than 10%. Expressed in symbolic form this is p < 0.10. Since
that statement does not contain a condition of equality, the original claim is the
alternative hypothesis. The null hypothesis is H0 : p = 0.10. Thus the Type I
error in this situation would be the mistake of rejecting the claim that at least
10% of students in the western US believe that Jim Morrison is still alive, when
in fact it is true that at least 10% of students in the western US believe that Jim
Morrison is still alive.
(b) Is the original claim the null or alternative hypothesis?
Based on the discussion in the answer to the previous point, the original claim is
the alternative hypothesis.
(c) Find the critical value for this hypothesis test.
Examining the alternative hypothesis H1 : p < 0.10 we determine that we are
conducting a left-tailed test. The significance level is α = 0.025. From the normal
probability table then the critical value of z is zα = −1.96.
(d) At the 0.025 significance level, test the claim that the true percentage is less than
10%.
Based on the survey data mentioned we see that the sample proportion of gun
owners favoring stricter gun laws is ˆp = 0.08. The value of test statistic is then
z0 =
ˆp − p
p(1−p)
n
= 0.08 − 0.10
(0.10)(1−0.10)
1245
≈ −2.35.
Since the test statistic falls in the critical region we reject the null hypothesis.
Therefore we conclude that the sample data support the claim that the percentage
of students in the western United States who believe that Jim Morrison is alive is
less than 10%.