Question

What is the difference in means between the "Number of errors while listening to music" and the "Number of errors with nomusic?" Explain the meaning of your answer in the context of the problem.

Answer 1

`\text{difference in means = 7.125}`Step-by-step explanation:

let the mean of numbers of errors while listening to music = μ1

let the mean of numbers of errors with no music = μ2

`\begin{gathered} \mu_1\text{ = }\frac{s\text{ um of the data}}{nu\text{mber of data}} \\ nu\text{mber of data = }8 \\ \mu_1\text{ = }(16+12+15+18+21+11+15+19)/(8) \\ \mu_1\text{ = }(127)/(8) \\ \mu_1\text{ = }15.875 \end{gathered}`
`\begin{gathered} \mu_2=\frac{s\text{ um of the data}}{nu\text{mber of data}} \\ nu\text{mber of data = }8 \\ \mu_2=(11+8+4+13+7+9+12+6)/(8) \\ \mu_2=(70)/(8) \\ \mu_2=8.75 \end{gathered}`
`\begin{gathered} \text{Difference in means = }\mu_2-\mu_1 \\ \text{Difference in means =}8.75\text{ - 15.875} \\ \text{Difference in means =}-7.125 \\ Since\text{ the difference is negative, we would take the absolute value:} \\ \text{Difference in means =}|-7.125| \\ \text{Difference in means =}7.125 \end{gathered}`

The difference in means shows the absolute difference between the mean value in two groups in a clinical trial.

The result shows the amount of difference between the average of experimental and control group.

The mean of all the difference of all the sample mean in the table is 7.125