Question

A random sample of 144 residents in a community produced 88 residents testing positive for the herpes simplex virus (which causes cold sores). Researchers wish to test whether proportion testing positive is different from .50. Use α=.05.

**Give each of the following to receive full credit**: 1) the appropriate null and alternative hypotheses; 2) the appropriate test; 3) the decision rule; 4) the calculation of the test statistic; and 5) your conclusion including a comparison to alpha or the critical value. What do the results mean? You MUST show your work to receive full credit. Partial credit is available.

Step 1

(1)

The test is conducted to check whether the proportion of people who shows positive test results (p) for the herpes of the simplex virus is different from 0.50 or not.

Therefore, the null and alternative hypothesis can be constructed as follows:

Step 2

(2)

The residents in the sample are independent and is collected randomly from the population.

Here, the hypothesis value of the population proportion (p_{o}) is 0.5 and the size of the sample (n) is 144. Therefore,

Step 3

(3)

Decision rule on the basis of the* p*-value is,

The null hypothesis will be rejected if the *p*-value is less than th...

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