Question

An automatic machine is set to fill bags of dog food with exactly 25 pounds on average with a standard deviation of 0.5 pounds. A random sample of 100 bags was selected. The sample mean was found to be 24.85 pounds. Determine whether or not the machine is working properly using a 5% level of significance.

Answer 1

Answer:

Step-by-step explanation:

Given that an automatic machine is set to fill bags of dog food with exactly 25 pounds on average with a standard deviation of 0.5 pounds.

Sample size = n =100

x bar = 24.85 pounds

Sample std error = $\frac{\sigma}{\sqrt{n} } =0.05$

Hypotheses:

$H_0: x bar = 25\\H_a: x bar \neq 25$

(Two tailed test at 5% level)

Mean difference =0.15

Test statistic = mean diff/se = 3

Since population std dev is known z test can be used

p value =0.0000

Since p <0.05 we find that the bag does not contain exactly 25 pounds.