Question

A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 436.0 gram setting. It is believed that the machine is underfilling the bags. A 40 bag sample had a mean of 430.0 grams. A level of significance of 0.02 will be used. Is there sufficient evidence to support the claim that the bags are underfilled? Assume the standard deviation is known to be 23.023.0.

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :   = 436

H_a :    436

Test statistic = z

= ( - ) / / n

= (430 - 436) / 23 / 40

= -1.65

Test statistic = -1.65

P(z < -1.65) = 0.0495

P-value = 2 * 0.0495 = 0.099

= 0.02  

P-value >

Fail to reject the null hypothesis .

There is not sufficient evidence to support the claim that the bags are underfilled .