Respuesta :
Answer:
The null hypothesis is [tex]H_o: p \leq 0.2[/tex]
The alternate hypothesis is [tex]H_a: p > 0.2[/tex]
The pvalue of the test is 0.1515 > 0.01, which means that we do not reject the null hypothesis that 20% of less users develop nausea, that is, we have no sufficient evidence that this proportion is larger than 20%.
Step-by-step explanation:
Test the claim that more than 20% of users develop nausea
This means that the null hypothesis is that 20% or less of the users develop nausea, that is:
[tex]H_o: p \leq 0.2[/tex]
And the alternate hypothesis is that more than 20% develop, so:
[tex]H_a: p > 0.2[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
0.2 is tested at the null hypothesis:
This means that [tex]\mu = 0.2, \sigma = \sqrt{0.2*0.8}[/tex]
Suppose 229 subjects are treated with a drug that is used to treat pain and 52 of them develop nausea.
This means that [tex]n = 229, X = \frac{52}{229} = 0.2271[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.2271 - 0.20}{\frac{\sqrt{0.2*0.8}}{\sqrt{229}}}[/tex]
[tex]z = 1.03[/tex]
Pvalue of the test an decision:
Probability of finding a proportion above 0.2271, which is 1 subtracted by the pvalue of z = 1.03
Looking at the z-table, z = 1.03 has a pvalue of 0.8485
1 - 0.8485 = 0.1515
The pvalue of the test is 0.1515 > 0.01, which means that we do not reject the null hypothesis that 20% of less users develop nausea, that is, we have no sufficient evidence that this proportion is larger than 20%.
