26lb. a)Find the best point estimate of the mean weight of the population of all

Question

26lb. a)Find the best point estimate of the mean weight of the population of all men. b)Construct a 95% confidence interval of the true mean weight of all men. Assume that we want to estimate the mean IQ score for the population of statistics students. How many statistics students must be randomly selected for IQ tests if we want 90% confidence that the sample mean is within 5 IQ points of the population mean? 5) The amount of lateral expansion (mils) was determined for a sample of n 9 pulsed-power gas metal arc welds used in LNG ship containment tanks. The resulting sample standard deviation was s 2.80 mils. Assuming normality, derive a 95% CI for 2 and for Lioht hulhs of a certain tvpe are advertised as having an average lifetime of 800 hours. The price of these

Explanation / Answer

Q5.

CONFIDENCE INTERVAL FOR STANDARD DEVIATION
ci = (n-1) s^2 / ^2 right < ^2 < (n-1) s^2 / ^2 left
where,
s = standard deviation
^2 right = (1 - confidence level)/2
^2 left = 1 - ^2 right
n = sample size
since alpha =0.05
^2 right = (1 - confidence level)/2 = (1 - 0.95)/2 = 0.05/2 = 0.025
^2 left = 1 - ^2 right = 1 - 0.025 = 0.975
the two critical values ^2 left, ^2 right at 8 df are 17.5345 , 2.18
s.d( s )=2.8
sample size(n)=9
confidence interval for ^2= [ 8 * 7.84/17.5345 < ^2 < 8 * 7.84/2.18 ]
= [ 62.72/17.5345 < ^2 < 62.72/2.1797 ]
[ 3.5769 < ^2 < 28.7746 ]

and confidence interval for = sqrt(lower) < < sqrt(upper)
= [ sqrt (3.5769) < < sqrt(28.7746), ]
= [ 1.8913 < < 5.3642 ]

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