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Chapter 4: Q. 99 (page 281)

I work out a lot Are people influenced by what others say? Michael conducted an experiment in front of a popular gym. As people entered, he asked them how many days they typically work out per week. As he asked the question, he showed the subjects one of two clipboards, determined at random. Clipboard A had the question and many responses written down, where the majority of responses were6or7days per week. Clipboard B was the same, except most of the responses were1or2days per week. The mean response for the Clipboard A group was4.68and the mean response for the Clipboard B group was4.21.

a. Calculate the difference (Clipboard A 鈥� Clipboard B) in the mean number of days for the two groups. One hundred trials of a simulation were performed to see what differences in means would occur due only to chance variation in the random assignment, assuming that the responses on the clipboard don鈥檛 matter. The results are shown in the dotplot.

b. There is one dot at0.72. Explain what this dot means in this context.

c. Use the results of the simulation to determine if the difference in means from part (a) is statistically significant. Explain your reasoning.

Short Answer

Expert verified

(a) 0.47is the difference in the mean number of days for the two groups.

(b) The dot signifies that the difference between clipboard A and clipboard B is greater.

(c) The difference in mean is not statistically significant because other factors also influence the result.

Step by step solution

01

Part (a) Step 1: Given Information -

We are given the mean response for Clipboard A=4.68and the mean response for Clipboard B=4.21and we have to find out the difference in the mean number of days.

02

Part (a) Step 2: Explanation

According to the question,

Mean (Clipboard A - Clipboard B)

We have, mean=4.68-4.21

On solving, we get, mean=0.47

Hence, 0.47is the difference in the mean number of days for the two groups.

03

Part (b) Step 1: Given Information

We are given the mean response for Clipboard A=4.68and the mean response for Clipboard

B=4.21 and we have to find out the explanation of dot.

04

Part (b) Step 2: Explanation

The dot0.72 signifies that the difference in the Clipboard A and Clipboard B is more. Its depicts that the responses mentioned for the question are very different from each other.

05

Part (c) Step 1: Given Information

We are given the mean response for Clipboard A=4.68and the mean response for Clipboard

B=4.21and we have to find out if the difference is statistically significant.

06

Part (c) Step 2: Explanation

Using the results of the simulation to determine if the difference in means from part (a) is statistically significant, we conclude that the difference is statistically not significant. The result can be influenced by many other factors as well. Accuracy can't be achieved only by analyzing the difference. Hence other method to evaluate the survey should be considered to produce better result.

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