Question

A manufacturer of coffee vending machines has designed a new, less expensive machine. The current machine is known to dispense an average of 6 fl. oz., with a standard deviation of .2 fl. oz., into cups. When the new machine is tested using 15 cups, the mean and the standard deviation of the fills are found to be 6 fl. oz. and .212 fl. oz. Test H0: σ = .2 versus Ha: σ ≠ .2 at levels of significance .05 and .01. Assume normality. (Round your answer to 4 decimal places.) chi-square H0 for α = 0.05. H0 for α = 0.01.

Answer 1

Solution:

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

H₀: σ = .2 versus H_a: σ ≠ .2

This is a two tailed test.

We are given

α = 0.05 and 0.01

n = 15

Sample standard deviation = S = 0.212

Degrees of freedom = n – 1 = 14

The test statistic formula is given as below:

Chi square = (n – 1)*S^2/σ^2

Chi square = (15 - 1)* 0.212^2/0.2^2

Chi square = 15.7304

P-value = 0.3301

(by using Chi square table or excel)

P-value > α = 0.05

So, we do not reject the null hypothesis at α = 0.05

P-value > α = 0.01

So, we do not reject the null hypothesis at α = 0.01

There is insufficient evidence to conclude that population standard deviation is not equal to 0.2.