8. In a random sample of 53 concrete specimens, the average porosity (in percent

Question

8. In a random sample of 53 concrete specimens, the average porosity (in percent) was 21.6 and the standard deviation was 3.2. a. Find a 90% confidence interval for the mean porosity of specimens of this type of concrete. b. Find a 95% confidence interval for the mean porosity of specimens of this type of concrete. c. What is the confidence level of the interval (21.0,22.2)? d. 1 low many specimens must be sampled so that a 90% confidence interval Specifies the mean to within plus or minus 0.3? e. How many specimens must be sampled so that a 95% confidence interval specifies the mean to within plus or minus 0.3?

Explanation / Answer

m = 21.6

sd = 3.2

P(-inf. < Z < z) = 0.99

z = 2.33

x = 21.6 + 3.2 * 2.33

x = 29.056

so porosity upper bound limit is 29.05%,

ii.

x<22.7

z < (22.7 - 21.6)/3.2

z < 0.3437

P(z<0.3437) = 0.6331

So, 63.31% confidece level it is.

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