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. Find and enter the correct critical value needed to test your claim at the 5% significance level. Round your final answer to 4 decimals.

Answer 1

We are given

$\mu_s = 11.88\\ \sigma_s = 0.82\\ \alpha = 0.05/2 = 0.025$
n=400

Hypothesis

$H_0: \mu_s=12\\ H_1: \mu_s\le12$

Here we use a t-test since the population standard deviation is unknown.

$\\t-stat = \frac{\mu_s - 12}{\frac{0.82}{\sqrt{400}}}\\ t-stat = \frac{11.88 - 12}{\frac{0.82}{\sqrt{400}}} = -2.8915\\$

Using the t table we find the pvalue = 0.002021

T-critical value

We find the t-critical value using the table for p=0.025 and df = 399

t-critical = -1.96

Since the t-stat is less than t-critical, hence we reject the null hypothesis and conclude that the the machine is not filling the cans to the specified 12 ounces