Refer to the Journal of Food Engineering (Sep. 2013) study of the characteristics of fried sweet potato chips, Exercise 7.78. Recall that a sample of 6 sweet potato slices fried at 130º using a vacuum fryer yielded the following statistics on internal oil content (measured in gigagrams): y̅₁ = .178 g/g and s₁ = .011 g/g. A second sample of 6 sweet potato slices was obtained, only these were subjected to a two-stage frying process (again, at 130º) in an attempt to improve texture and appearance. Summary statistics on internal oil content for this second sample follows: y̅₂ = .140 g/g and s₂ = .002 g/g. The researchers want to compare the mean internal oil contents of sweet potato chips fried with the two methods; however, they recognize that the sample sizes are small.
a. What assumption about the data is required in order for the comparison of means to be valid?

b. Construct a 95% confidence interval for the ratio of the two population variances of interest.

c. Based on the interval, part b, is there a violation of the assumption, part a? Explain.

Data from Exercise 7.78

Refer to the IEICE Transactions on Information & Systems (Jan. 2005) experiment to monitor the impedance to leg movements, Exercise 7.34. Engineers attached electrodes to the ankles and knees of volunteers and measured the signal-to-noise ratio (SNR) of impedance changes. Recall that for a particular ankle–knee electrode pair, a sample of 10 volunteers had SNR values with a mean of 19.5 and a standard deviation of 4.7. Form a 95% confidence interval for the true standard deviation of the SNR impedance changes. Interpret the result.