Question

Pepsi is experimenting with a new machine that fills their cans with product three times faster than the previous method they were using. However, they are worried that the increase in speed might be because the machine is less accurate. You want to test if the machine is not filling the cans to the specified 12 ounces. You sample 400 cans filled by the new machine and find they fill the cans with an average 11.88 ounces with a standard deviation of 0.82 ounces.

Answer 1

It is given that

Sample mean is given as $\mu_{s}$=11.88

Sample standard deviation is given as $\sigma _{s}$=0.82

We have to find whether new machine not filling the cans specified 12 ounces

here lets consider 95% Confidence interval for which value of $\alpha$ will be 5%

Lets take the hypothesis testing

Null Hypothesis$H_{0\Rightarrow }$$\mu_{s}$=12

Alternate Hypothesis$H_{1\Rightarrow }$$\mu_{s}\leq 12$

Now use T-test

Because population standard deviation is unknown

$\Rightarrow t_{stat}$=$(\mu_{s}-12)/\sigma/\sqrt(n))$

=(11.88-12)/0.82/$\sqrt{400}$=-2.89

Using T-table

Value of p will be 0.002021

We find t critical value using table for p=0.25 and degree of freedom =(n-1)=(400-1)=399

So $t_{critical}=-1.96$

because $t_{stat}$ is less than $t_{critical}$

We will reject null hypothesis

We conclude that machine is not filling the cans to specified 12 ounces

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