100 people were surveyed to see their preference for chocolate candy bars among 5 brands. Use Chi-Square to test the data at the 0.05 significance level. What is the expected distribution? What is the null and alternative Hypotheses? Reece’s Snickers Hershey Bar Payday M&Ms Actual observed data: Reece’s Snickers Hershey Bar Payday M&Ms 25 30 12 9 24 Df= ____ Chi Square Critical Value: ______ Math, X2= 16.3 Interpretation: Reject or Fail to Reject the Null Hypothesis? Write a sentence describing your decision.
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Step 1
- Expected count for each brand = 100 / 5 = 20. - Expected distribution: 20, 20, 20, 20, 20 for Reece’s, Snickers, Hershey Bar, Payday, and M&Ms respectively. Show more…
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Chi-Square Test for Goodness-of-Fit The Consumer Affairs Department of Mars, Inc. says that the distribution of color for milk chocolate M&M's is as follows: red orange yellow green blue brown 12.5% 25% 12.5% 12.5% 25% 12.5% You wonder if the distribution of M&M colors in a large bag follows this same distribution, with significance level α = 0.05. So you take a random sample of 60 milk chocolate M&M's from a large bag, and you observe the following distribution of colors: red orange yellow green blue brown 3 9 7 9 20 12 State your null and alternative hypotheses: H0: Ha: How many M&M's of each color should you expect to find in a sample of 60 M&M's? red orange yellow green blue brown The chi-square statistic is a measure of how far the observed counts are from the expected counts. There are n = ____ colors of M&M's candies, so the degrees of freedom are df = ____ - 1 = ____. The χ² critical value (from the table) for df = ____ and α = ____ is ____. The χ² test statistic (from the calculator) is ____ and the p-value is ____. Based on the comparison of the test statistic and critical value, ____. Based on the comparison of the significance level and the p-value, ____. Conclusion: ____.
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Suppose a random sample of 320 students was asked to indicate which of the 4 candy items they preferred: York Mints, Peanut Butter Cups, Snickers, or Kit Kat. What is the calculated value of Chi-square? Question 12: How many degrees of freedom do you have? In Question 12, at the 0.05 level of significance, what would the critical value of Chi-square be? Be sure to round off to decimal places. In Question 12, at the 0.05 level of significance, should you reject the null hypothesis? (True/False) In Question 12, at the 0.05 level of significance, are the results statistically significant? (True/False)
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Conduct the hypothesis test and provide the test statistic and the critical value, and state the conclusion. A company claims that its packages of 100 candies are distributed with the following color percentages: 14% red, 20% orange, 16% yellow, 6% brown, 26% blue, and 18% green. Use the given sample data to test the claim that the color distribution is as claimed. Use a 0.01 significance level. What is the test statistic? What is the p-value? Candy Counts Color Number in Package Red 13 Orange 25 Yellow 9 Brown 7 Blue 27 Green 19 Chi-square: Degrees of Freedom 0.995 0.99 0.975 0.95 0.90 0.10 0.05 0.025 0.01 0.005 1 - - 0.001 0.004 0.016 2.706 3.841 5.024 6.635 7.879 2 0.010 0.020 0.051 0.103 0.211 4.605 5.991 7.378 9.210 10.597 3 0.072 0.115 0.216 0.352 0.584 6.251 7.815 9.348 11.345 12.838 4 0.207 0.297 0.484 0.711 1.064 7.779 9.488 11.143 13.277 14.860 5 0.412 0.554 0.831 1.145 1.610 9.236 11.071 12.833 15.086 16.750 6 0.676 0.872 1.237 1.635 2.204 10.645 12.592 14.449 16.812 18.548 7 0.989 1.239 1.690 2.167 2.833 12.017 14.067 16.013 18.475 20.278 8 1.344 1.646 2.180 2.733 3.490 13.362 15.507 17.535 20.090 21.955 9 1.735 2.088 2.700 3.325 4.168 14.684 16.919 19.023 21.666 23.589 10 2.156 2.558 3.247 3.940 4.865 15.987 18.307 20.483 23.209 25.188
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