Question

workers at a certain soda drink factory collected data on the volumes in oz of a simple random sample of 15 cans of a soda drink. these values have a mean of 12.19oz and a standard deviation of 0.08 oz and they appear to be from a normally distributed population. if the want the filing process to work so that almost all cans have volumes between 11.93 oz and 12.56oz, the range rule of thumb can be used to estimate that the standard deviation should be less than 0.16oz. use the sample data to test the claim that the population of volumes has a standard deviation less than 0.16oz. use a 0.025 significance level

Answer 1

Let denotes the true population standard deviation.

To test against

Here

sample standard deviation

and sample size

The test statistic can be written as

which under H₀ follows a chi square distribution with n-1 df.

We reject H₀ at 0.025 significance level if P-value < 0.025

Now,

The value of the test statistic

P-value =

Since P-value < 0.025, so we reject H₀ at 0.025 significance level and we can conclude that there is enough evidence to support the claim that the population of volumes has a standard deviation less than 0.16oz.