Question

2. A machine that fills beverage cans is supposed to put 12 ounces of beverage in each can. Following are the amounts measured in a simple random sample of eight cans. 11.96 12.10 12.04 12.13 11.98 12.05 11.91 12.03 A dotplot of the sample data suggests that the population is approximately normal. Perform a hypothesis test to determine whether the mean volume differs from 12 ounces. Use the a= 0.05 level of significance. (a) State the null and alternate hypotheses. (b) Compute the value of the test statistic. (c) Find the P-value of the test statistic. (d) Make the decision to reject or fail to reject the null hypothesis. (e) Write a conclusion statement.

Answer 1

a)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 12
Alternative Hypothesis, Ha: μ ≠ 12

b)

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (12.025 - 12)/(0.0727/sqrt(8))
t = 0.973

c)

P-value Approach
P-value = 0.3630

d)

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

e)

There is not sufficient evidence to conclude that the mean differs from 12 ounces