Question

In a study testing the effects of placebos (sugar pills) on the headaches of 995 participants, when the participant believed that the pill was expensive, it was found that 327 participants had reduced pain after 30 minutes. We wish to test the claim that the actual proportion is different than 0.80 at the α=0.11 level of significance. What is the test statistic? Answer in decimal form. Round to 4 decimal places as needed.

Answer 1

As we are testing here whether the actual proportion is different than 0.80, therefore the test statistic here is computed as:

Therefore -37.17 is the required test statistic value here.

As this is a two tailed test, the p-value here is computed from the standard normal tables as:

p = 2P(Z < -37.17) = approx. 0

As the p-value here is approx. 0 < 0.11 which is the level of significance, therefore the test is significant and we can reject the null hypothesis here. We have sufficient evidence here that the proportion is different from 0.8.