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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.

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.

check_circleAnswer
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:

Null hypothesis
H p 0.5
That is, the population proportion of people showing positive test results is 0.5.
Alternate hypothesis:
H p 0.50
That is, the population proportion of people showing positive test results is
different from 0.5.
help_outline

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Null hypothesis H p 0.5 That is, the population proportion of people showing positive test results is 0.5. Alternate hypothesis: H p 0.50 That is, the population proportion of people showing positive test results is different from 0.5.

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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 (po) is 0.5 and the size of the sample (n) is 144. Therefore,

npo 144(0.5)
=72
10
Therefore, all the necessary conditions are satisfied for performing a z- test for a
population proportion: Hence, the appropriate test is the z- test for a population
proportion
help_outline

Image Transcriptionclose

npo 144(0.5) =72 10 Therefore, all the necessary conditions are satisfied for performing a z- test for a population proportion: Hence, the appropriate test is the z- test for a population proportion

fullscreen
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...

p (Z>z)
= 2 x P
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p (Z>z) = 2 x P

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Statistics

Hypothesis Testing

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