What if it is 99% confidence? What if it is 90% confidence? from a nationally kn

Question

What if it is 99% confidence?

What if it is 90% confidence?

from a nationally known manufacturer. The manufacturer's specifications state that the standard deviation of the amount of paint is equal to 0.02 gallon. A random sample of 50 cans is selected, and the sample mean amount of paint per 1-gallon can is 0.989 gallon. Complete parts (a) through (d). a. Construct a 95% confidence interval estimate for the population mean amount of paint included in a 1-gallon can. (Round to five decimal places as needed.)

Explanation / Answer

Given:-
M = 0.989
Z = 1.96
sM = (0.022/50) = 0.00283
Therefore, the 95% confidence interval for mean is,
= M ± Z(sM)
= 0.989 ± 1.96*0.00283
= 0.989 ± 0.00554

Result

M = 0.989, 95% CI [0.98346, 0.99454].

You can be 95% confident that the population mean () falls between 0.98346 and 0.99454.

# Therefore the 99% confidence interval for mean is,

= M ± Z(sM)
= 0.989 ± 2.58*0.00283
= 0.989 ± 0.00729

Result

M = 0.989, 99% CI [0.98171, 0.99629].

You can be 99% confident that the population mean () falls between 0.98171 and 0.99629

# Therefore the 90% confidence interval for mean is,

= M ± Z(sM)
= 0.989 ± 1.64*0.00283
= 0.989 ± 0.00465

Result

M = 0.989, 90% CI [0.98435, 0.99365].

You can be 90% confident that the population mean () falls between 0.98435 and 0.99365.

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