Question

Show your work please

A random sample of 20 aluminum cola cans is selected and the axial loads are measured and the variance is 345.96 lb. Use a 0.05 significance level to test the claim that cans have axial loads with the smaller variance than 772.84 lb.

final answers

Hypothesis
Test Statistic
p-value
Decision
Conclusion

Answer 1

Here, we have to use Chi square test for the population variance or standard deviation.

The null and alternative hypotheses for this test are given as below:

Null hypothesis: H0: The cans have axial loads with the variance than greater than or equal to 772.84 lb.

Alternative hypothesis: Ha: The cans have axial loads with the smaller variance than 772.84 lb.

H0: σ2 ≥ 772.84 versus Ha: σ2 < 772.84

This is a lower tailed test.

The test statistic formula is given as below:

Chi-square = (n – 1)*S^2/ σ2

From given data, we have

n = 20

S^2 = 345.96

σ2 = 772.84

Chi-square =(20 - 1)*345.96/772.84 = 8.5053

Chi-square = 8.5053

We are given

Level of significance = α = 0.05

df = n – 1

df = 19

Critical value = 10.1170

(by using Chi square table or excel)

P-value = 0.0192

(by using Chi square table or excel)

P-value < α = 0.05

So, we reject the null hypothesis

There is sufficient evidence to conclude that the cans have axial loads with the smaller variance than 772.84 lb.