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A researcher claims that the incidence of a certain type of cancer is less than 5%. To test this claim, the a random sample of 4000 people are checked and 170 are determined to have the cancer. The following is the setup for this hypothesis test: JH : p=0.05 (H: p<0.05 Find the test statistic for this hypothesis test for a proportion. Round your answer to 2 decimal places.

Respuesta :

Answer: The test statistic value is -0.95.

Step-by-step explanation:

Since we have given that

[tex]H_0:p=0.05\\\\H_a:p<0.05[/tex]

Here, n = 4000

x = 170

So, [tex]\hat{p}=\dfrac{170}{4000}=0.0425[/tex]

So, Test statistic value would be

[tex]\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}\\\\=\dfrac{0.0425-0.05}{\sqrt{\dfrac{0.5\times 0.5}{4000}}}\\\\=-0.95[/tex]

Hence, the test statistic value is -0.95.