A schoolteacher would like to know whether or not toothpaste brands are used dif

Question

A schoolteacher would like to know whether or not toothpaste brands are used differentially in her classroom (in other words, is one brand preferred over the others?). She asks her students to report which of three brands they use: Crest, Colgate, or Aquafresh. Below are the numbers of students who use each type of toothpaste (notice there are 45 students total in her class). Test her hypothesis using an alpha level of .05. a. What test is appropriate for this analysis? b. State the null hypothesis: c. State the alternative hypothesis: d. Find the critical value: e. Calculate the test statistic: f. Make a decision:

Explanation / Answer

a. The Chi- square test for indpendence will be aprropriate for this analysis

b.Null Hypothesis : H0 : There is no specifice preference for any brand of toothpaste among students.

c. Alternative Hypothesis : Ha : There is specific preference for brands of toothpaste among students.

d. Critical Value of chi- square for dF =2 and alpha = 0.05

X2critical = 5.991

e. Expected value of toothpaste users for each brand = 15

X2 = (24 - 15)2 /15 + (13-15)2 /15 + (8 -15)2 /15 = 8.933

f. so here X2 > X2critical so we can reject the null hypothesis and can say that students have specific preference over toothpaste brands.

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