A manufacturer of salad dressings uses machines to dispense liquid ingredients into bottles that move along a filling 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. 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 significance in the analysis should be 99%.

Step-by-step explanation:

From the given information:

The null hypothesis is:

The alternative hypothesis is:

The sample size n = 35

Sample mean = 7.91

variance = 0.03

Standard deviation =

The t-test statistics is computed as:

t = - 3.0741

Degree of freedom:

df = n - 1

df = 35 - 1

df = 34

Level of significance = 1 - C.I

= 1 - 0.99

= 0.01

The t_{critical} value for the two-tailed test at 0.01 is within the rejection region:

Decision rule: To reject if  

As fails the rejection region, we reject

Conclusion: There is sufficient evidence to believe that the machine will not dispense 8 ounces & and it must be stopped for repairs.

a framing bias

step-by-step explanation:

rodrigo is subject to a framing bias i believe.