Question

A soft drink filling machine, when in perfect alignment, fills the bottles with 12 ounces of soft drink. A random sample of 36 bottles is selected, and the contents are measured. The sample yielded a mean content of 11.75 ounces with a standard deviation of 0.75 ounces.

a) Formulate the hypothesis to test to determine if the machine is in perfect adjustment.

b) Compute the value of the test statistic

c) Compute the p-value and give your conclusion regarding the adjustmentof the machine. Let a= 0.05.

On this problem the instructor has stated "For each question listed, explain how to get the correct answer. Think of this like an essay question. Or like you’re tutoring somebody. That’s what I’m really shooting for—for you to understand the material well enough to explain it to somebody else. If you can show me you can do that, you will get full credit.

So the answer has to be in essay form or comprehensive form. explaining the variables and how i got to the answer.

Answer 1

a) H₀: = 12

    H₁: 12

b) The test statistic t = ()/(s/)

                                 = (11.75 - 12)/(0.75/)

                                 = -2

c) P-value = 2 * P(T < -2)

                 = 2 * 0.0267

                 = 0.0534

Since the P-value is greater than the significance level (0.0534 > 0.05), so we should not reject the null hypothesis.

So there is sufficient evidence to conclude that the machine is in perfect alignment.