Question

A company claims that the mean volume of the soda in its cans is 12.0 ounces. In a random sample of 8 of its cans, the mean is found to be 12.1 ounces. Based on past research, the population standard deviation is assumed to be 0.1 ounces. Test the claim that the mean is 12.0 ounces. Use a 0.01 level of significance.

a) State the null and alternative hypotheses.

b) Find the value of the test statistic. Use the appropriate formula and show your work. Round to three decimal places.

c) Find the P-value. Use normalcdf and sketch a curve to accompany your answer. Round to three decimal places.

d) State whether you should reject or fail to reject the null hypothesis. Justify your answer.

e) State your conclusion in non-technical terms.

Answer 1

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

b)
Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (12.1 - 12)/(0.1/sqrt(8))
z = 2.83

c)
P-value = 0.005

d)
As P-value < 0.01, reject the null hypothesis.

e)
There is sufficient evidence to conclude that the mean is different than 12 ounces