Question

Use the given claim to identify the Null Hypothesis, the Alternative Hypothesis, test statistics, P-value or Critical Values, then state the conclusion about the null hypothesis as well as the final conclusion that addresses the original claim The Brazil vending machine dispenses coffee, and a sample random sample of 27 filled cups have contents with a mean of 7.14 oz. and a standard deviation of 0.17 oz. Use a 0.05 significance level to test the claim that the machine dispenses amounts with a standard deviation of 0.15 oz. specified in the machine design d.f. Н, : Н;: Test statistic P-value Critical Value Graph: Conclusion Interpretation

Answer 1

Solution:

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

From given data and information, we have

n = 27

df = n – 1 = 27 – 1 = 26

α = 0.05

H₀: The machine dispenses amounts with a standard deviation of 0.15 oz. specified in the machine design.

H_a: The machine dispenses amounts with a standard deviation different than 0.15 oz. specified in the machine design.

H₀: σ = 0.15

H₁: σ ≠ 0.15

Test statistic:

Chi square = (n – 1)*S^2/σ^2

We are given n = 27, S = 0.17

Chi square = (27 - 1)*0.17^2 / 0.15^2

Chi square = 33.39556

Test statistic: 33.39556

P-value = 0.150929

Critical value = 13.8439 and 41.9232

(by using Chi square table or excel)

Graph:

pdf P-va ue P-value 13.8439 33.39556 41.9232 Test statistic

Conclusion:

P-value = 0.150929 > α = 0.05

So, we do not reject the null hypothesis

Interpretation:

There is sufficient evidence to conclude that the machine dispenses amounts with a standard deviation of 0.15 oz. specified in the machine design.