Question

Step 1 of 3: A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 432 gram setting. It is believed that the machine is underfilling the bags. A 39 bag sample had a mean of 426 grams. Assume the population standard deviation is known to be 26. At level of significance of 0.05 we have the test : H0: μ ≥ 432, H0: μ < 432 Choose the value of the test statistic to the second decimal place:

Answer 1

The value of the test statistic is
`t = -1.44`

Explanation:

The null hypothesis is:

`H_(0) \geq 432`

The alternate hypotesis is:

`H_(1) < 432`

Our test statistic is:

`t = (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.

In this problem, we have that:

`X = 426, \mu = 432, \sigma = 26, n = 39`

So

`t = (X - \mu)/((\sigma)/(√(n)))`

`t = (426 - 432)/((26)/(√(39)))`

`t = -1.44`

The value of the test statistic is
`t = -1.44`