Question

A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 430 430 gram setting. It is believed that the machine is underfilling the bags. A 27 27 bag sample had a mean of 429 429 grams with a standard deviation of 13 13 . A level of significance of 0.025 0.025 will be used. Assume the population distribution is approximately normal. Is there sufficient evidence to support the claim that the bags are underfilled? Answer 2 Points.

Answer 1

Solution :

= 430

=429

S =13

n = 27

This is the left tailed test .

The null and alternative hypothesis is ,

H₀ :    = 430

H_a : < 430

Test statistic = t

= ( - ) / S / n

= (429-430) / 13 / 27

= −0.4

Test statistic = t = −0.4

P-value =0.3463

= 0.05  

P-value >

0.3463 > 0.025

Fail to reject the null hypothesis .

There is not sufficient evidence toclaim that the population mean μ is less than 430, at the 0.025 significance level.