SOLUTION: A simple random sample from a population with a normal distribution of 106 body temperatures has x =98.90 degrees and s =0.61 degrees. Construct a 95​% confidence interval es

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Question 1131798: A simple random sample from a population with a normal distribution of 106 body temperatures has x =98.90 degrees and s =0.61 degrees. Construct a 95​% confidence interval estimate of the standard deviation of body temperature of all healthy humans.
Answer by rothauserc(4718)   (Show Source): You can put this solution on YOUR website!
sample size(n) is 106 body temperatures
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degrees of freedom = 106 - 1 = 105
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the mean of the sample is 98.90
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standard deviation of the sample is 0.61
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We use the chi-square distribution to construct the 95% confidence interval(CI) for the population standard deviation
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alpha(a) = 1 -(95/100) = 0.05
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critical probability(p*) = 1 -(a/2) = 0.975
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chi-square(0.975) = 78.536
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chi-square(0.025) = 135.247
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population variance(0.975) = ((106-1)*(0.61)^2)/78.536 = 0.4975
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population variance(0.025) = ((106-1)*(0.61)^2)/135.247 = 0.2889
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take the square roots to get standard deviation
:
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the 95% confidence interval is (0.5375, 0.7053)
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