Question

A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 442 gram setting. It is believed that the machine is underfilling the bags. A 44 bag sample had a mean of 438 grams. Assume the population variance is known to be 576. A level of significance of 0.1 will be used. You may write the P-value as a range using interval notation, or as a decimal value rounded to four decimal places.

Answer 1

H0: = 442 ,

Ha: < 442

Test statistics

z = - / / sqrt(n)

= 438 - 442 / ( sqrt(576) / sqrt(44) )

= -1.11

This is test statistics value

p-value = P( Z < z)

= P( Z < -1.11)

= 0.1335

Since p-value > 0.1 significance level, we do not have sufficient evidence to reject H0.

We conclude at 0.1 level that we fail to support the claim.