A soft drink machine is regulated so that the amount of drink it dispenses follo

Question

A soft drink machine is regulated so that the amount of drink it dispenses follows a normal distribution with a known standard deviation, and it is believed that standard deviation of the drinks dispensed is 20 milliliters.
However a random sample of 30 drinks from the machine produced an average value of 373 milliliters and standard deviation of 23.4 milliliters; therefore, based on the results from sample data, there is concern that population standard deviation might be higher than what is believed.
Check the validity of the concern by determining a 95% confidence interval for the standard deviation of all drinks dispensed by this machine.

Explanation / Answer

population standard deviation of the drinks dispensed , = 20 milliliters.
sample size, n = 30

sample average , x = 373

sample standard deviation , s = 23.4

Null Hypothesis, Ho: <= 20

Alternate hypothesis, Ha: > 20

since we are comparing standard deviation, we will use chi square test to determine whether the hypothesis is true or not.

degree of freedom, df = n-1 = 30-1 = 29

at 95% confidence for a right tail distribution, critical statistics chi square = 42.557

test statistics = (n-1)(s/)2 = (30-1)(23.4/20)2

= 39.6981

since test statistics is less than the critical statistics and this is an upper one-tailed alternative, we accept the null hypothesis.

Hence the concern that population standard deviation might be higher than what is believed is false.

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