*** Shown below is an explanation for why my answers are wrong. The mean and sta
ID: 3239836 • Letter: #
Question
*** Shown below is an explanation for why my answers are wrong.
The mean and standard deviation of a random sample of n measurements are equal to 33.5 and 3.2, respectively. a. Find a 95% confidence interval for u if n 64 b. Find a 95% confidence interval for H if n 256. c. Find the widths of the confidence intervals found in parts a and b. What is the effect on the width of a confidence interval of quadrupling the sample size while holding the confidence coefficient fixed a. The 95% confidence in rval for H if n 64 is approximately (32.701.34.3 tel (Round to three decimal places as needed.)Explanation / Answer
Solution:-
The formula for estimation is:
= M ± Z(sM)
where:
M = sample mean
Z = Z statistic determined by confidence level
sM = standard error = (s2/n)
Calculation
M = 33.5
t = 1.96
sM = (3.22/64) = 0.4
= M ± Z(sM)
= 33.5 ± 1.96*0.4
= 33.5 ± 0.784
You can be 95% confident that the population mean () falls between 32.716 and 34.284.
(b) Calculation
M = 33.5
t = 1.96
sM = (3.22/256) = 0.2
= M ± Z(sM)
= 33.5 ± 1.96*0.2
= 33.5 ± 0.392
You can be 95% confident that the population mean () falls between 33.108 and 33.892.
(c) Width -
for (a) where n = 64
34.284 - 32.716 = 1.568
Width for (b) where n = 256
33.892 - 33.108 = 0.784
As, the sample size increases the data becomes a better and better representator of the population, hus given more precise results.
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