Respuesta :
Answer:
1. z = 0.184
2. P-value = 0.427
3. The null hypothesis is that the proportion of treated subjects that experienced headaches is not significantly higher than 9%.
The null hypothesis is failed to be rejected.
4. At a significance level of 0.01, there is not enough evidence to support the claim that more than 9% of treated subjects experienced headaches.
Step-by-step explanation:
This is a hypothesis test for a proportion.
The claim is that more than 9% of treated subjects experienced headaches.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi=0.09\\\\H_a:\pi>0.09[/tex]
The significance level is 0.01.
The sample has a size n=275.
The sample proportion is p=0.095.
[tex]p=X/n=26/275=0.095[/tex]
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.09*0.91}{275}}\\\\\\ \sigma_p=\sqrt{0.000298}=0.017[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p-\pi-0.5/n}{\sigma_p}=\dfrac{0.095-0.09-0.5/275}{0.017}=\dfrac{0.003}{0.017}=0.184[/tex]
This test is a right-tailed test, so the P-value for this test is calculated as:
[tex]\text{P-value}=P(z>0.184)=0.427[/tex]
As the P-value (0.427) is greater than the significance level (0.01), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that more than 9% of treated subjects experienced headaches.
