The filling machine for a production operation must be adjusted if more than 10% of the items being produced

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The filling machine for a production operation must be adjusted if more than 10% of the items being produced are under filled. A random sample of 100 items from day’s production contained 16 under filled items. Does the sample evidence indicate that the filling machine should be adjusted? Conduct an appropriate test of hypotheses for the population proportion using an alpha value of .05. use minitab output to help answer.

- Write the null and alternative hypotheses.

- State the rejection rule for the null hypothesis using the “critical value method to test hypothesis”.

- State the rejection rule for the null hypothesis using the “p-value method to test hypothesis”.

- State your statistical conclusion as it relates to the problem and in words relating to the problem. 

Test and CI for one proportion

Test of p = 0.1 vs p > 0.1

Sample                        X         N         Sample p         lower bound    Z-value            P-value

1                                 16        100       0.160000         0.099699            2.00                 0.023