Question

A machine that is programmed to package 1.202 pounds of cereal is being tested for its accuracy in a sample of 36 cereal boxes, the sample mean filling weight is calculated as 1.22 pounds. The population standard deviation is known to be 0.06 pounds. Which of the following conclusions is correct? A. The machine is operating improperly because the target is below the lower limit. B. The machine is operating properly because the interval contains the target. C. The machine is operating improperly because the target is above the upper limit. D. There is not enough information to make a conclusion.

Answer 1

Solution :

= 1.202

= 1.22

=0.06

n = 36

This is the two tailed test .

The null and alternative hypothesis is ,

H0 :    = 1.202

Ha :     1.202

Test statistic = z

= ( - ) / / n

= (1.22-1.202) / 0.06 / 36

= 1.8

Test statistic = z =1.8

P(z > 1.8 ) = 1 - P(z < 1.8 ) = 1 -0.9641

P-value = 2 *0.0359 =0.0718

B ) The machine is operating properly because the interval contains the target.