Pupillometer is a device used to observe changes in an individual’s pupil dilations as he or she is exposed different visual stimuli. A Research Laboratory used a pupillometer to evaluate consumer reaction to different silverware patterns for one of its client companies. Suppose 15 consumers were chosen, and each was shown two different silverware patterns. The pupil dilation for each pattern shown was measured and their difference was computed. The sample mean of the differences in pupil dilation per consumer between silverware patterns 1 and 2 was 0.2393 mm and the sample standard deviation of the differences was 0.1608 mm. (a) Construct a 90% confidence interval to estimate the true difference in mean pupil dilation per consumer for silverware patterns 1 and 2 in the population. (b) What assumptions are required for the confidence interval of part (a) to be statistically valid?

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A Pupillometer is a device used to observe changes in an individual’s pupil dilations as he or she is exposed different visual stimuli. A Research Laboratory used a pupillometer to evaluate consumer reaction to different silverware patterns for one of its client companies. Suppose 15 consumers were chosen, and each was shown two different silverware patterns. The pupil dilation for each pattern shown was measured and their difference was computed. The sample mean of the differences in pupil dilation per consumer between silverware patterns 1 and 2 was 0.2393 mm and the sample standard deviation of the differences was 0.1608 mm.

(a) Construct a 90% confidence interval to estimate the true difference in mean pupil dilation per consumer for silverware patterns 1 and 2 in the population.
(b) What assumptions are required for the confidence interval of part (a) to be statistically valid?

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