MATH SOLVE

3 months ago

Q:
# The producer of a certain medicine claims that its bottling equipment is very accurate and that the standard deviation of all its filled bottles is 0.1 ounce or less. A sample of 20 bottles showed a standard deviation of .11. The test statistic to test the claim is _____.

Accepted Solution

A:

Answer: The test statistic to test the claim is [tex]\chi^2=22.99[/tex].Step-by-step explanation:Let [tex]\sigma[/tex] be the standard deviation of filled bottles.As per given , we have[tex]H_0:\sigma=0.1\\\\ H_1:\sigma\neq0.1[/tex]To fins test statistic , we use Chi -square test for population standard deviation:[tex]\chi^2=\dfrac{(n-1)s^2}{\sigma^2}[/tex], where n= sample size .s= sample standard deviation.We are given that , n= 20 and s= 0.11Then, [tex]\chi^2=\dfrac{(20-1)(0.11)^2}{(0.1)^2}[/tex] [tex]\chi^2=\dfrac{(19)(0.0121)}{0.01}=22.99[/tex]Hence, the test statistic to test the claim is [tex]\chi^2=22.99[/tex].