Question

A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 434 gram setting. It is believed that the machine is underfilling the bags. A 9 bag sample had a mean of 431 grams with a variance of 144. A level of significance of 0.01 will be used. Assume the population distribution is approximately normal. Is there sufficient evidence to support the claim that the bags are underfilled

Answer 1

No, there is not sufficient evidence to support the claim that the bags are underfilled

Explanation:

A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 434 gram setting.

This means that the null hypothesis is:

`H_(0): \mu = 434`

It is believed that the machine is underfilling the bags.

This means that the alternate hypothesis is:

`H_(a): \mu < 434`

The test statistic is:

`z = (X - \mu)/((\sigma)/(√(n)))`

In which X is the sample mean,
`\mu` is the value tested at the null hypothesis,
`\sigma` is the standard deviation and n is the size of the sample.

434 is tested at the null hypothesis:

This means that
`\mu = 434`

A 9 bag sample had a mean of 431 grams with a variance of 144.

This means that
`X = 431, n = 9, \sigma = √(144) = 12`

Value of the test-statistic:

`z = (X - \mu)/((\sigma)/(√(n)))`

`z = (431 - 434)/((12)/(√(9)))`

`z = -0.75`

P-value of the test:

The pvalue of the test is the pvalue of z = -0.75, which is 0.2266

0.2266 > 0.01, which means that there is not sufficient evidence to support the claim that the bags are underfilled.