Question

A manufacturer of chocolate chips would like to know whether its bag filling machine work correctly at the 420 gram setting. He believed that the machine is underfilling or overfilling the bag. A 49 bag sample had a mean of 423 grams. Assume the population variance is known to be 676. Is there sufficient evidence at the 0.02 level of significance that the bags are overfilled?

H0 =

Ha =

Test Statistic (round your answer to two decimal places): z =

Test Type (write L for left-tailed, R for right-tailed, and T for two-tailed):

Critical z-values :

Conclusion (write R for "reject H0", and F for "fail to reject H0"):

Answer 1

Solution:

1)

H₀ : = 420

H_a : > 420

2)

Test statistic z is given by

z = [ - ]/[ ]

= [423 - 420]/[(676/49)]

= 0.81

z = 0.81

3)

Test type : R

4)

For right tailed test , the critical value is

Critical z value : 2.054

5)

Conclusion : F

(because 0.81 < 2.054 )