Question

A manufacturer of banana chips would like to know whether its bag filling machine works correctly...

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.

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Answer #1

Solution :

This is the two tailed test .

The null and alternative hypothesis is ,

H0 :   = 436

Ha :    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 .

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