Question

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 were$6$or$7$days per week. Clipboard B was the same, except most of the responses were$1$or$2$days per week. The mean response for the Clipboard A group was$4.68$and the mean response for the Clipboard B group was$4.21$.

a. Calculate the difference (Clipboard A – 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’t matter. The results are shown in the dotplot.

b. There is one dot at$0.72$. 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

(a) $0.47$is 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

Part (a) Step 1: Given Information -

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

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

Part (b) Step 1: Given Information

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

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

Part (b) Step 2: Explanation

The dot$0.72$ 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.

Part (c) Step 1: Given Information

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

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

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.