Question

Is the machine working correctly? The machine is set up to dispense, on average, 1.20 ounces of garlic powder into each bottle. The manager at this factory is trying to assess its accuracy. Upon examining a sample of 36 bottles, he finds that the average is 1.22 ounces with a sample standard deviation of 0.07 ounces. a. Select the null and the alternative hypotheses to determine if the machine is working improperly, that is, it is either underfilling or overfilling the garlic powder bottle. Но: и 2 1.20; Нд: и < 1.20 Но: и < 1.20; НА: и> 1.20 Ho: u = 1.20; HA: µ # 1.20 O b-1. Calculate the value of the test statistic. (Round answer to 2 decimal places.) 0.54 X Test statistic b-2. Find the p-value. (Round answer to 4 decimal places.) 0.3742 X p-value c-1. What is the conclusion at a 5% significance level? Reject Ho since the p-value is greater than significance level. * Reject Ho since the p-value is smaller than significance level. O Do not reject Ho since the p-value is greater than significance level. Do not reject Ho since the p-value is smaller than significance level.

Please show work with Excel formulas

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 1.2
Alternative Hypothesis, Ha: μ ≠ 1.2

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (1.22 - 1.2)/(0.07/sqrt(36))
t = 1.71

P-value Approach
P-value = 0.0961

=2*(1-T.DIST(1.71,35,TRUE))

As P-value >= 0.05, fail to reject null hypothesis.

option C