A machine pours soda into 12-ounce bottles. If the standard deviation of the amount of soda poured exceeds 0.23 ounces, then this is an indication that the machine is not working correctly. To see if the machine is working correctly, a random sample of 20 bottles of soda is taken and the number of ounces in each of these samples is given in Table 4.13.

a. Does the standard deviation exceed 0.23 ounces?

b. How big of a sample would be needed to find at least a 0.30-ounce difference in the standard deviation?

c. Is a sample size of \(n=20\) large enough to find at least a 0.07 difference in the standard deviation?

Table 4.13

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Number of Ounces in a Random Sample of 20 12-Ounce Bottles of Soda 12.35 12.41 12.30 12.04 12.33 12.06 12.04 12.05 12.33 12.09 12.22 12.05 12.00 12.06 12.85 12.31 12.22 12.04 12.25 12.36