Question

A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 405 gram setting. It is believed that the machine is underfilling the bags. A 42 bag sample had a mean of 398 grams. Assume the population variance is known to be 841. A level of significance of 0.05 will be used. Find the P-value of the test statistic. You may write the P-value as a range using interval notation, or as a decimal value rounded to four decimal places.

Answer 1

Solution :

Given that,

= 398 gram

= 841 =  29 gram

n = 42

Hypothesis:

H0 : = 405

Ha : < 405

Test Statistic:

   Z = ( - ) / ( /n)

   Z = (398 - 405) / ( 29/ 42 )

  Z = -1.56

The test statistic is -1.56

Reject H0 if P-value     = 0.05

P-value =0.0594

fail to reject H0. There is insufficient evidence to support the claim.

0.05 < p-value< 1.0