Question 1199574: A research wants to determine if pre-natal exposure to the hormones in birth control pills alters the sex makeup of midshipman fish populations (which are typically half male and half female).
Specifically, the researcher wishes to test the hypothesis that exposure to hormones will increase the number of females in the population.
The researcher exposes a group of pregnant midshipman fish to birth control hormones and records the sex of the first 14 offspring birthed.
They then observe that 4 are female.
Use a sign test and a alpha of .05 to test the indicated hypothesis.
What is the critical value?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! null hypothesis is .5 females and .5 males.
sample size is 14
standard error is equal to (.5 * .5 / 14) ^ .5 = .1336.
critical z-score at .05 alpha on the high end is equal to 1.645.
test z-score is (4/14 - .5) / .1336 = -1.6039
area to the right of that z-score is equal to .9456.
this is well abobve the critical alpha os .05, therfore the conclusion is that the hormones do not increasde the number of females in the population.
in fact, it appears that the hormones decrease the number of females in the population.
null hypothesis is .5 females and .5 males.
sample size is 14.
standard error i equal to (.5 * .5 / 14) ^ .5 = .1336.
test z-score is (4/14 - .5) / .1336 = -1.6039.
area to the left of that z-score is equal to .054.
this is slightly greater than the critical alpha of .05, therefore the conclusion is that the hormones do not decrease the number of females in the population, although the results are much closer to being significant than the test that the hormones increase the number of females in the population.
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