The drug Symbicort is used to treat asthma. In a clinical trial of Symbicort, 18 of 277 treated
subjects experienced headaches, according to the manufacturer AstraZeneca. Test the claim that
less than 10% of treated subjects experienced headaches. Use the 0.05 level of significance.
a)
𝐻0 : 𝑃 = 0.1
𝐻1 : 𝑃 < 0.1
b)
Critical Value: This is a left-tailed test, and the critical value is -1.645
c)
𝑝̂ =
18
277
= 0.065
Test Statistic (Z) =
𝑃̂ −𝑃
𝑝𝑞
√
𝑛
=
0.065−0.1
(0.1)(0.9)
277
= -1.943
√
d)
P-Value = 0.026
e)
Reject the null hypothesis. Since the test statistic (-1.943) is smaller than the critical value (1.645), and since the p-value (0.026) is smaller than alpha (0.05), then we reject the null
hypothesis and conclude that more than 10% of treated subjects experienced headaches.
f)
At the 5% level of significance, there is insufficient evidence to support the claim that less than
10% of treated subjects experienced headaches