The amount of bleach a machine pours into bottles has a mean of 36 oz. With a standard deviation of 0.15 oz. Suppose we take a random sample of 36 bottles filled by this machine. The sampling distribution of the sample mean has a standard error of 0.15
Answer: The given statement "The sampling distribution of the sample mean has a standard error of 0.15" is false.
The sampling distribution of the sample mean is:
[tex]\sigma_{\bar{x}}=\frac{\sigma}{\sqrt{n}}[/tex]
We are given:
The standard deviation, [tex]\sigma =0.15[/tex]
[tex]n=36[/tex]
[tex]\therefore \sigma_{\bar{x}}=\frac{0.15}{\sqrt{36}}[/tex]
[tex]=0.025[/tex]
Therefore, the sampling distribution of the sample mean has a standard error of 0.025.
Hence the given statement is false.
