The filling machine for a production operation must be adjusted if more than 8% of the items being produced are underfilled. A random sample of 80 items from the day’s production contained nine underfilled items. Does the sample evidence indicate that the filling machine should be adjusted? Use a level of significance of 0.01.

The p value is given by:

For this case the p value is higher than the significance level of 0.01 so then we have enough evidence to FAIl to reject the null hypothesis and we can't conclude that the true proportion is significanctly higher than 8%

Step-by-step explanation:

Information given

n=80 represent the random sample taken

X=9 represent the number fo items undefilled

estimated proportion of underfilled items

is the value that we want to test

represent the significance level

z would represent the statistic

represent the p value

Hypothesis to test

We want to test if the true proportion of items underfilled is higher than 0.08 and we got.:  

Null hypothesis:  

Alternative hypothesis:  

The statistic is given by:

(1)  

Replacing the info given by:

The p value is given by:

For this case the p value is higher than the significance level of 0.01 so then we have enough evidence to FAIl to reject the null hypothesis and we can't conclude that the true proportion is significanctly higher than 8%

step-by-step explanation: