Answer:
Reject <em>H</em>₀. 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, <em>α</em> = 0.02.
(1)
The hypothesis can be defined as follows:
<em>H</em>₀: There is no difference between the proportions of drug-resistant cases in the two states, i.e. 
.
<em>Hₐ</em>: There is a statistically significant difference between the proportions of drug-resistant cases in the two states, i.e. 
.
(2)
Compute the sample proportions and total proportion as follows:
Compute the test statistic value as follows:
![Z=\frac{\hat p_{1}-\hat p_{2}}{\sqrt{\hat p(1-\hat p)\times [\frac{1}{n_{1}}+\frac{1}{n_{2}}]}}](https://tex.z-dn.net/?f=Z%3D%5Cfrac%7B%5Chat%20p_%7B1%7D-%5Chat%20p_%7B2%7D%7D%7B%5Csqrt%7B%5Chat%20p%281-%5Chat%20p%29%5Ctimes%20%5B%5Cfrac%7B1%7D%7Bn_%7B1%7D%7D%2B%5Cfrac%7B1%7D%7Bn_%7B2%7D%7D%5D%7D%7D)
![=\frac{0.063-0.019}{\sqrt{0.032(1-0.032)\times [\frac{1}{189}+\frac{1}{429}]}}\\\\=2.86](https://tex.z-dn.net/?f=%3D%5Cfrac%7B0.063-0.019%7D%7B%5Csqrt%7B0.032%281-0.032%29%5Ctimes%20%5B%5Cfrac%7B1%7D%7B189%7D%2B%5Cfrac%7B1%7D%7B429%7D%5D%7D%7D%5C%5C%5C%5C%3D2.86)
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:
<em>p</em>-value = 0.00424 < <em>α</em> = 0.02.
The null hypothesis will be rejected at 0.02 significance level.
Reject <em>H</em>₀. There is a significant difference in drug resistance between the two states.
