Respuesta :
Answer:
Claim is False that the incidence of fatigue is greater among those who use Clarinex.
Step-by-step explanation:
Let [tex]p_1[/tex] and [tex]p_2[/tex] be the probabilities of the the incidence of fatigue of those using Clarinex. and placebos respectively
2% of the 1650 treated subjects experienced fatigue who are using Drug Clarinex.
[tex]n_1[/tex] = 1650
[tex]\widehat{p_1}=0.02[/tex]
[tex]y_1=2\% \times 1650 =33[/tex]
Among the 1600 subjects given placebos, 1% experienced fatigue.
[tex]n_2[/tex] = 1600
[tex]\widehat{p_2}=0.01[/tex]
[tex]y_21\% \times 1600 =16[/tex]
Claim : The incidence of fatigue is greater among those who use Clarinex.
[tex]H_0:p_1\leq p_2\\H_a:p_1>p_2[/tex]
We will use Comparing Two Proportions
[tex]\widehat{p}=\frac{y_1+y_2}{n_1+n_2} =\frac{33+16}{1600+1650}=0.015[/tex]
Formula of test statistic :[tex]\frac{\widehat{p_1}-\widehat{p_2}}{\sqrt{\widehat{p}(1-\widehat{p})(\frac{1}{n_1}+\frac{1}{n_2})}}[/tex]
Substitute the values
test statistic :[tex]\frac{0.02-0.01}{\sqrt{0.015(1-0.015)(\frac{1}{1650}+\frac{1}{1600})}}[/tex]
test statistic :2.344
refer z table for p value
p value = 0.9904
α = 0.05
Since p value >α
So, we accept the null hypothesis
So, the claim is wrong that the incidence of fatigue is greater among those who use Clarinex.
