Question

1. Consumer reports would like to see if customers prefer one brand of potato chips over others. In a recent report it was discovered that 25 chose Lay’s, 13 chose Cape Cod, and 12 chose the generic brand. Are customer’s choices different for the different brand of potato chips?

1. State the null and alternative hypothesis for the above survey.
2. Create a frequency table with all the choices labeled
3. Choose the correct test and find the observed value.
4. Compare the observed to the critical value.
5. What is the conclusion in APA format?

Answer 1

Solution: Null Hypothesis: Alternative Hypothesis: Customer's choices are different for the different brand of potato chips Customer's choices are same for the different brand of potato chips In symbolic form HoiPlays 3 Ha: At least one of the proportion is different form the others - pcapecod PGeneric If the null hypothesis is true, expected frequencies can be calculated as below: Observed Frequency 0 25 13 12 Expected Frequency o- E(o - E)2 (0 E)/E 4.167 0.807 1.307 Brand 50 x 1/3 16.667 50 x 1/3 16.667 50 x 1/3 16.667 YE 50 Lay's Cape Cod Generic 8.333 3.667 4.667 69.444 13.444 21.778 2 0 -50 6.280 Chi-square test would be the correct test Observed Chi-square test statistic: 6.280 Degrees of Freedom df (Total number of categories -1) Hence, df 3 1 2

Critical value: Let significance level a 0.05 From the x2 distribution table; the critical value of x2, having area in the upper tail equal to 0.05 and for (df 2), is given by: 5.991 Hence, Xeritical 5.991 Conclusion: since observed value of test statistic χ2-6280 is more than the critical value of χ2tical-5.991, we reject the null hypothesis There is sufficient evidence to conclude that customer's choices are different for the different brand of potato chips