SOLUTION: A survey claims that 9 out of 10 doctors recommend aspirin for their patients with headaches. To test this claim against the alternative that the actual proportion of doctors who

Question 118449: A survey claims that 9 out of 10 doctors recommend aspirin for their patients with headaches. To test this claim against the alternative that the actual proportion of doctors who recommend aspirin is less than 0.90, a random sample of 100 doctors results in 84 who indicate that they recommend aspirin. The value of the test stastistic in this problem is approximately equal to:
A. -4.12
B. -2.33
C. -1.86
D. -0.07
Answer by wgunther(43) (Show Source): You can put this solution on YOUR website!
Our null hypothesis is that our sample proportion, p, is .9. Our alternative hypothesis is p<.9.
We know by the CLT, that because we have a large sample size, the distribution of the sample proportion is approximately normal. So, the test statistic, as usual, is the difference between the sample proportion and the actual proportion, divided by standard error, assuming the null hypothesis. In this case, as distribution is binormal, we know the standard error is assuming the null hypothesis of course. So, the test statistics would be
So, the answer is probably C, -1.86. We know the p-value is somewhere between .01 (-1.65 critical value) and .05 (-2.33 critical value) so this is actually kind of a gray area where we hesitant about rejecting the null hypothesis because it isn't statistically significant at the 5% alpha level, but is at the 1% alpha level.
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