Answer to Question #121402 in Statistics and Probability for Areesha Ashraf

Question

A machine is a set to fill cereal boxes with the mean weight of 500 grams of cereal per box The standered deviation is known to be 25 grams. A random sample of 100 filled boxes is taken and the mean weight of cereal per box is computed as 504 grams. Is there reason to believe that machine is over filing the boxes use a=0.05

Answer 1

Given: $\overline{x}$ }=504,n=100, $\mu _{0}$ =500, $\sigma$  = 25

Step 1: state the hypothesis

H0: μ=500

H1: μ>500

Step 2:Name of the test

since population standard deviation is known, we use one sample z test.

Step 3: Test statistic:

z= $\frac{\overline{x}-\mu _{0}}{\frac{\sigma}{\sqrt{n}}}$

=$\frac{504-500}{\frac{25}{\sqrt{100}}}$

=1.6

Step 4: Critical value:

since H1 has >, it is right tailed test, so find 1-a=1-0.05=0.95 

Look up the area from Step in the z-table. The area is at z=1.645. This is your critical value for a confidence level of 5%

Step 5: conclusion:

since test statistic < critical value , null hypothesis is not rejected

Therefore, there is not enough evidence to claim that the population mean 

μ is greater than 500, at the 0.05 significance level.