Question

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.

Answer 1

Answer:

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/$\sqrt{35}$=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 .