Question

. A manufacturer of cell batteries claims that the life of the company's batteries os approximately normally distributed with a standard deviation equal to 0.8 year. If a random sample of 12 batteries has a standard deviation of 1.4 years, do you think that σ > 0.8 ? Use a 0.05 level of significance.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: σ = 0.8
Alternative Hypothesis, Ha: σ > 0.8

Rejection Region
This is right tailed test, for α = 0.05 and df = 11
Critical value of Χ^2 is 19.675
Hence reject H0 if Χ^2 < 19.675

Test statistic,
Χ^2 = (n-1)*s^2/σ^2
Χ^2 = (12 - 1)*1.4^2/0.8^2
Χ^2 = 33.688

P-value Approach
P-value = 0.0004
As P-value < 0.05, reject the null hypothesis.