Question

A manufacturer of salad dressings uses machines to dispense liquid ingredients into bottles

that move along a lling line. The machine that dispenses salad dressings is working properly when 8

ounces are dispensed. Suppose that the average amount dispensed in a particular sample of 35 bottles

is 7.91 ounces with a variance of 0.03 ounces squared (= 0.173). Is there evidence that the machine

should be stopped and production wait for repairs? The lost production from a shutdown is potentially

so great that management feels that the level of signi cance in the analysis should be 99%

Answer 1

Step 1:

Ho: = 8

Ha:   8

Null hypothesis states that the 8 ounces per machine.

Step 2: Test statistics

n = 35

sample mean = 7.91

variance = 0.03; sample sd = sqrt (0.03) = 0.173

Assuming that the data is normally distributed, also as the population sd is not given we will calcuate t stat.

Step 3:

df = 35-1 = 34

level of significance.  = 0.01

The t-critical values for a two-tailed test, for a significance level of α=0.01

tc = − 2.728 and tc = 2.728

As the t stat (-3.074) falls in the rejection area, we reject the Null hypotheisis.

Hence there is sufficient evidence to believe that the machine is not dispensing 8 ounces and shoud be stopped for repairs.