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The fitness of 514 adults (aged 25 to 35) were sampled and their heart rates measured...

The fitness of 514 adults (aged 25 to 35) were sampled and their heart rates measured immediately after exercise. This sample of adults was found to have a mean of 1427 beats (per 10 minutes) with a standard deviation of 325 beats (per 10 minutes).

Construct a two-tailed 95% confidence interval for the true mean heart beat of all such adults.

Determine the sample size that would be necessary to obtain an interval with width (at most) 50 for a confidence level of 95%.

Let assume the sample is from a normal population, and sample size is 30 instead of 514. Construct a

99% upper tail confidence interval for the true mean heart beat of all such adults.

math   Statistics-And-Probability   
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Answer #1

Mean= 1417

Std= 325

n= 514

a) 95% Confidence interval: t_{alpha /2,n-1}=t_{0.05,513}=1.964599

CI: ar{X}pm t*(S/sqrt{n})=>1427pm 1.964599*(325/sqrt{514})

CI (1398.837,1455.163)

b) ME= 50

ME=2* Z*(S/sqrt{n})=> n= (rac{2*Z*S}{ME})^2= (rac{2*1.96*325}{50})^2= 649

c) n=30

99% Confidence interval: t_{alpha ,n-1}=t_{0.01,29}=2.462021

UCI:ar{X}+ t*(S/sqrt{n})=>1427+ 2.462021(325/sqrt{30})

UCI:1573.088

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