Question

Aluminum cans. The axial load of a can of aluminum is the maximum weight that sides can support before collapsing. Axial load is an important measure as the top covers exert pressure on the sides with pressures ranging from 158 to 165 pounds. Pepsi experimented with a random sample of 175 cans with an average axial load of 267.11 pounds. Standard cans have an average axial load of 281.81 pounds and a standard deviation of 27.77 pounds. Use a significance level of 0.01 to test the claim that the cans have a mean axial load other than 281.81 lbs.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 281.81
Alternative Hypothesis, Ha: μ ≠ 281.81

Rejection Region
This is two tailed test, for α = 0.01
Critical value of z are -2.576 and 2.576.
Hence reject H0 if z < -2.576 or z > 2.576

Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (267.11 - 281.81)/(27.77/sqrt(175))
z = -7

P-value Approach
P-value = 0

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

There is sufficient evidence to conclude that the cans have a mean axial load other than 281.81 lbs.