Question 1200977: A doctor claims that the standard deviation of systolic blood pressure is 12 mmHg. A random sample of 24 patients found a standard deviation of 14 mmHg. Assume the variable is normally distributed. At alpha=0.01, what are the critical χ2 values?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the claim is that the standard deviation is 12 mmhg.
sample of 24 patients found a standard deviation of 14 mmhg.
the standard deviation is presumed to have a normal distribution.
since the sample size is 24, then the standard error is equal to the population standard deviation divided by the square root of the sample size = 12/sqrt(24) = 2.449489743.
the z-score formula is z = (x-m)/s
z is the z-score
x is the sample mean
m is the population mean
s is the standard error
the z-score formula becomes z = (14 - 12) / 2.449489743 = .8164965809.
the area to the right of that z-score is equal to .2071080281.
since the critical alpha on the high end of the confidence interval is less than that, the results are not significant and the decision is that there is not enough evidence to indicate that the standard deviation is not 12 mmhg.
note that, even if your alpha on the high end was .01, the results would still not be significant and the conclusion would be the same (there is not enough evidence to indicate that the standard deviation is not 12 mmhg).
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