Consider a machine that produces metal pieces which are
cylindrical in shape. We select
a sample of nine pieces and measure the diameters:
1.01; 0.97; 1.03; 1.04; 0.99; 0.98; 0.99; 1.01; 1.03
The sample and sample standard deviation are x̄ = 1.00556 and s =
0.02455, respectively.
Give a 95% confidence interval for the true mean diameter, assume
that the
population is normal.
Solution :
Given that,
=1.00556
s = 0.02455
n = 9
Degrees of freedom = df = n - 1 = 9 - 1 = 8
At 95% confidence level the t is ,
= 1 - 95% = 1 - 0.95 = 0.05
/ 2 = 0.05 / 2 = 0.025
t /2,df = t0.025,8 =2.306
Margin of error = E = t/2,df * (s /n)
= 2.306 * (0.02455 / 9)
= 0.01887
Margin of error = 0.01887
The 99% confidence interval estimate of the population mean is,
- E < < + E
1.00556 - 0.01887 < <1 .00556 + 0.01887
0.9867 < < 1.0244
(2.70, 3.70 )
Consider a machine that produces metal pieces which are cylindrical in shape. We select a sample...
Consider a machine that produces metal pieces which are cylindrical in shape. We select a sample of nine pieces and measure the diameters: 1.01, 0.97, 1.03, 1.04, 0.99, 0.98, 0.99, 1.01, 1.03 The sample and sample standard deviation are T = 1.00556 and s = 0.02455, respec- tively. Give a 95% confidence interval for the true mean diameter, assume that the population is normal. A. (0.989,1.022] B. (0.978,1.033] C. (0.991,1.034] D. (0.987,1.024] E. none of the preceding
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