High School

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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 \(4\) days per week. Clipboard B was the same, except most of the responses were \(2\) days per week. The mean response for the Clipboard A group was \(x\) and the mean response for the Clipboard B group was \(y\).

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 \(z\). 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.

Answer :

The answers are:

a. The difference would be X - Y.
b. Since there is only one dot, it means that this particular difference in means occurred only once out of the 100 trials of the simulation.

c. If the observed difference falls within the extreme tails of the distribution, it suggests that the difference is unlikely to occur by chance alone. Thus, it would be statistically significant.

a. To calculate the difference in the mean number of days for the two groups, we subtract the mean response of Clipboard B from the mean response of Clipboard A. Let's say the mean response for Clipboard A is X and the mean response for Clipboard B is Y.


b. The dot on the dotplot represents the difference in means that occurred due to chance variation in the random assignment.

c. To determine if the difference in means from part (a) is statistically significant, we need to compare it with the distribution of differences in means from the simulation. However, without specific values or more information about the dotplot and the distribution, it's difficult to determine the statistical significance.

In conclusion, we calculated the difference in means between the two groups, discussed the meaning of a dot in the context of the dotplot, and mentioned the importance of comparing the observed difference with the distribution to determine statistical significance.

Learn more about dotplot from the given link:

https://brainly.com/question/28273786

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Rewritten by : Barada