Question

questions 13 through 15 refer to the following. a study was conducted to determine the power of a new chemical to increase the quality of olfactory sensations in humans. participants were asked to rate the quality of a chocolate bar, before and after inhaling the chemical on a scale of 1 to 10, with 1 meaning low quality and 10 meaning high quality. analysis of the data showed that the difference in perceived quality of the chocolate bar before and after exposure to the chemical was statistically significant. perceived quality of chocolate bar

participant #	before exposure to chemical	after exposure to chemical	difference (after - before)
2	6	10	4
3	3	6	3
4	6	9	3
5	5	7	2
			mean difference = 3 standard deviation = 0.71

13 mark for review if these data were plotted on a graph, what percent of the scores for the difference in perceived quality of the chocolate bar are within 2.29 and 3.71? a 50 b 68 c 95 d 99.7

Explanation:

Step1: Recall the empirical rule

In a normal - distribution, approximately 95% of the data lies within 2 standard deviations of the mean.

Step2: Calculate the range around the mean

The mean difference is 3 and the standard deviation is 0.71. 2 standard deviations is \(2\times0.71 = 1.42\). The range within 2 standard deviations of the mean is \(3 - 1.42=1.58\) to \(3 + 1.42 = 4.42\). 1 standard deviation is \(0.71\), and the range within 1 standard deviation of the mean is \(3-0.71 = 2.29\) to \(3 + 0.71=3.71\). In a normal - distribution, approximately 68% of the data lies within 1 standard deviation of the mean.

Answer:

B. 68