Question

A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 413 gram setting. It is believed that the machine is underfilling of overfilling the bags. A 22 bag sample had a mean of 417 grams with a standard deviation of 13. Assume the population is normally distributed. A level of significance of 0.05 will be used. Specify the type of hypothesis test.

Answer 1

The decision rule is

Fail to reject the null hypothesis

The conclusion is

There is insufficient evidence to conclude that the machine is under filling the banana chips.

Explanation:

From the question we are told that

The population mean is
`\mu = 413 \ g`

The sample size is n = 22

The sample mean is
`\= x = 417 \ g`

The standard deviation is
`s = 13`

The level of significance is
`\alpha = 0.05`

The null hypothesis is
`H_o : \mu = 413`

The alternative hypothesis is
`H_a : \mu < 413 \ g`

Generally the test statistics is mathematically represented as

`z = (\= x - \mu )/( (s)/(√(n) ) )`

=>
`z = (417 - 413)/( (13)/(√(22) ) )`

=>
`z = 1.443`

Generally from the z table the probability of
`(Z > 1.443 )` is

`p-value = P(Z > 1.443) = 0.07451`

From the value obtained we can see that
`p-value > \alpha` hence

The decision rule is

Fail to reject the null hypothesis

The conclusion is

There is insufficient evidence to conclude that the machine is under filling the banana chips.