Question

A manufacturer of coffee vending machines has designed a new, less expensive machine. The current machine is known to dispense an average of 5 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 5 fl. oz. and .213 fl. oz. Test H₀: σ = .2 versus H_a: σ ≠ .2 at levels of significance .05 and .01. Assume normality.

Answer 1

Answer:

Given that:

When the new machine is tested using 15 cups, the mean and the standard deviation of the fills are found to be 5 fl. oz. and .213 fl. oz. Test H₀: σ = .2 versus H_a: σ ≠ .2 at levels of significance .05 and .01.

The null and alternative hypotheses are,

Here,    is the hypothesized  standard deviation.

Let the level of significance be    =0.05 and 0.01

Let the sample standard deviation be s = 0.213

Let the sample size be n = 15

The test statistic is  

So, the value of test statistic is 15.855

The degree of freedom is

df = n-1

df = 15-1

df = 14

Find the two tailed p-value for the test statistic

The p-value is greater than 0.01 and 0.05. Fail to reject the null hypothesis.

Therefore, at 1% and 5% level of significance there is no sufficient evidence to conclude that the standard deviation of coffee vending machine differs from 0.2fl.oz