Question 1198922: Among 157 African-American men, the mean systolic blood pressure was 146 mm Hg with a standard deviation of 27. We wish to know if on the basis
of these data, we may conclude that the mean systolic blood pressure for a population of African-American is greater than 140.
What is the null and alternative hypothesis?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! test mean = 140
sample size is 157
sample mean is 146 with standard deviation of 27
standard error = standard deviation / square root of sample size = 27 / sqrt(157) = 2.1548 rounded to 4 decimal places.
t = (x - m) / s = (146 - 140) / 2.1548 = 2.78448 rounded to 5 decimal places
t is the t-score
x is the sample mean
m is the test mean
s is the standard error
area to the right of that t-score with 156 degrees of freedom = .00301 rounded to 5 decimal places.
that's the test alpha.
at 99% one tail on the right confidence interval, the critical alpha is .01.
since the test alpha of .003 is less than that, you can conclude that the mean systolic blood pressure for a population of african americans is greater than 140.
the null hypothesis stated that the mean systolic blood pressure for african americans is not greater than 140.
the alternative hypothesis states that the mean systolic blood pressure for african americans is greater than 140.
since the test alpha was less than the critical alpha, the results of the test were considered significant and the null hypothesis was rejected in favor of the alternate hypothesis.
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