Respuesta :
Answer:
Reject H₀. There is a significant difference in drug resistance between the two states.
Step-by-step explanation:
In this case we need to determine whether the data suggest a statistically significant difference between the proportions of drug-resistant cases in the two states.
The significance level of the test is, α = 0.02.
(1)
The hypothesis can be defined as follows:
H₀: There is no difference between the proportions of drug-resistant cases in the two states, i.e. [tex]p_{1} - p_{2}= 0[/tex].
Hₐ: There is a statistically significant difference between the proportions of drug-resistant cases in the two states, i.e. [tex]p_{1} - p_{2}\neq 0[/tex].
(2)
Compute the sample proportions and total proportion as follows:
[tex]\hat p_{1}=\frac{12}{189}=0.063\\\\\hat p_{2}=\frac{8}{429}=0.019\\\\\hat p=\frac{12+8}{189+429}=0.032\\[/tex]
Compute the test statistic value as follows:
[tex]Z=\frac{\hat p_{1}-\hat p_{2}}{\sqrt{\hat p(1-\hat p)\times [\frac{1}{n_{1}}+\frac{1}{n_{2}}]}}[/tex]
[tex]=\frac{0.063-0.019}{\sqrt{0.032(1-0.032)\times [\frac{1}{189}+\frac{1}{429}]}}\\\\=2.86[/tex]
The test statistic value is 2.86.
(3)
The decision rule is:
The null hypothesis will be rejected if the p-value of the test is less than the significance level.
Compute the p-value as follows:
[tex]p-value=2\cdot P(Z>2.86)=2\times 0.00212=0.00424[/tex]
p-value = 0.00424 < α = 0.02.
The null hypothesis will be rejected at 0.02 significance level.
Reject H₀. There is a significant difference in drug resistance between the two states.
