Question

A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 430 gram setting. It is believed that the machine is overfilling the bags. A 37 bag sample had a mean of 439 grams. Assume a population standard deviation of 29. Is there sufficient evidence at the 0.05 level that the bags are overfilled? 24. Step 1. State the hypotheses: Ho: Step 2. Find the value of the z test statistic. (Round your answer to 2 decimal places.)

Answer 1

The hypotheses are

$H_0:\mu \leqslant 430\\ H_1:\mu >430\\$

The $\left ( 1-\alpha \right )100\%$ CI for mean is $\overline{x}\pm z_{1-\alpha }\frac{\sigma }{\sqrt{n}}$ .

The test statistic is

$z=\frac{\overline{x}-430}{\frac{\sigma }{\sqrt{n}}}\\ z=\frac{439-430}{29/\sqrt{37}}\\ {\color{Blue} z=1.888}$

This is a right tailed test. Hence One-tailed test

The P-value is

$\textup{P-value}=P\left ( z >1.888\right )\\ \textup{P-value}=1-\Phi \left ( 1.888\right )\\ {\color{Blue} \textup{P-value}= 0.0295}$

The level of significance is $\alpha =0.05$ .

Since $\textup{P-value}= 0.0295<0.05=\alpha$ ,

We Reject the null Hypothesis. (A).