## Related questions with answers

Hands-on soap bubble experiments are a great way to teach mathematics. In an effort to find the best possible bubble solution, two different soap concentrations were used along with two different amounts of glycerin additive. Students were then given a flat glass plate and a straw and were asked to blow their best bubbles. The diameters of the resulting bubbles (in millimeters) are listed below. Can an interaction be concluded between the soap solution and the glycerin? Is there a difference in the mean length of bubble diameter with respect to the concentration of soap to water? With respect to the amount of glycerin additive? Use $\alpha=0.05$.

$\begin{array}{|l|l|} \hline &+1\text{ Unit glycerin} &+2\text{ Units glycerin}\\ \hline \text{Soap:water 13:25}&115,113,105,110 & 98,100,90,95\\ \hline \text{Soap:water 1:2}&90,102,100,98 & 99,100,102,95 \\ \hline \end{array}$

Perform these steps. Assume that all variables are normally or approximately normally distributed, that the samples are independent and that the population variances are equal.

a. State the hypotheses. b. Find the critical value for each $F$ test. c. Complete the summary table and find the test value. d. Make the decision. e. Summarize the results. (Draw a graph of the cell means if necessary.)

Solution

VerifiedThe goal of this exercise is to utilize two-way ANOVA to determine whether the claim in this problem is supported by the traditional hypothesis testing approach. Remember the five stages of hypothesis testing to accomplish this. To obtain the critical values, use the $F$ distribution table, and then calculate the test statistic using the methodical process described in this chapter's lesson.

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