Answer:
The test statistic is z = 1.865.
Step-by-step explanation:
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
H0: p = 0.11
This means that 0.11 is tested at the null hypothesis, and so:
[tex]\mu = 0.11[/tex]
[tex]\sigma = \sqrt{0.11*0.89} = 0.3129[/tex]
The engineer weighs 94 bags and finds that 16 of them are over-filled.
This means that:
[tex]n = 94, X = \frac{16}{94} = 0.1702[/tex]
What is the test statistic?
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.1702 - 0.11}{\frac{0.3129}{\sqrt{94}}}[/tex]
[tex]z = 1.865[/tex]
The test statistic is z = 1.865.
