A machine used to fill gallon-sized paint cans is regulated so that the amount of paint dispensed has a mean of 123 ounces and a standard deviation of 0.30 ounce. You randomly select 35 cans and carefully measure the contents. The sample mean of the cans is 122.9 ounces. Does the machine need to be reset? Explain your reasoning.

There no need to restart the machine .

Step-by-step explanation:

Given: Mean at start =123 ounces

after the 35 cans selected means become 122.9 ounces .

and standard deviation of 0.30.

To find : Is there need to restart machine ?

Solution:

Standard error for mean is given by

Sm=Standard deviation /sqrt of number of samples(n)

   =0.30/=0.0507

Sm=0.0507

Now

for there is change in mean after 35 cans are selection hence there should be change in "t score "

which means t score =converting the individual of 35 cans to standard form.

it given by, with 5.07 % of the standard form

Change in mean /Sm= (122.9-123)/0.0507=1.9723

Then for the value of the   p =function of t score and the degree of freedom.

                                                =0.056

i.e. p>0.01 which means there no need to restart the machine .