The manager of a paint supply store wants to estimate the ac

The manager of a paint supply store wants to estimate the actual amount of paint contained in 1-gallon cans purchased from a nationally known manufacturer. The manufacturer’s specifications state that the standard deviation of the amount of paint is equal to 0.03 gallon. A random sample of 36 cans is selected and the sample mean amount of paint per 1-gallon can is 0.998 gallon.

Construct a 95% confidence interval estimate for the population mean amount of paint included in a 1-gallon can.

Step 1: figure out a point estimate x-bar:

Step 2: Is (population standard deviation) known? If yes, then find sample size n and /n

Step 3: find the confidence level (1-) and the critical value z_(1-/2).

Step 4: construct a confidence interval for population mean (the actual amount of paint contained in 1-gallon cans purchased). Please interpret the confidence interval.

Solution

Confidence Interval
CI = x ± Z a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
point estimate x-bar(x)=0.998
Standard deviation( sd )=0.03
Sample Size(n)=36
Confidence Interval = [ 0.998 ± Z a/2 ( 0.03/ Sqrt ( 36) ) ]
= [ 0.998 - 1.96 * (0.005) , 0.998 + 1.96 * (0.005) ]
= [ 0.988,1.008 ]