19. In a random sample of n - 1200 consumers who are surveyed about their ice cr
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Question
19. In a random sample of n - 1200 consumers who are surveyed about their ice cream flavor preferences, 416 indicate that they prefer vanilla, 419 prefer chocolate, and 365 prefer strawberry. (a) Conduct a Chi-squared "Goodness-of-Fit" Test of the null hypothesis of equal proportions Ho. Vanilla- Chocolate-Zgtrawberry of flavor preferences, at the = .05 significance level. Chocolate Strawberry Vanilla 416 419 365 1200 (b) Suppose that the sample of n = 1200 consumers is equally divided between males and females, yielding the results shown below. Conduct a Chi-squared Test of the null hypothesis that flavor preference is not associated with gender, at the = .05 level. Chocolate Strawberry Totals Males Females Totals Vanilla 200 216 416 190 229 419 210 155 365 600 600 1200Explanation / Answer
(a)
The Hypothesis:
H0: pvanilla = pchocolate = pstrawberry = 400.
Ha: At least 1 of the population proportions is not equal to 400.
The Test Statistic: The table below gives the calculation of 2. Each expected value = 1200/3 = 400
2test = 4.605
The Critical Value: The critical value at = 0.05 , degrees of freedom = c-1 = 2
2critical = 5.99
The Decision Rule: If 2 test is > 2 critical, then Reject H0.
The Decision: Since If 2 test is (4.605) < 2 critical (5.99), We Fail to reject H0.
The Conclusion: There is insufficient evidence at the 95% significance level to conclude that at least 1 of the population proportions is not equal to 400.
(b) The Observed and expected values are as below: Each Expected value is = Row Total*Column Total/N.
N = 1200
The Hypothesis:
H0: There is no relation between flavour preference and gender.
Ha: There is a relation between flavour preference and gender.
The Test Statistic: The table below gives the calculation of 2.
2test = 12.53
The Critical Value: The critical value at = 0.05, degrees of freedom = (r – 1) * (c -1) = ( 2 - 1) * ( 3 - 1) = 2
2critical = 5.99
The Decision Rule: If 2 test is > 2 critical, then Reject H0.
The Decision: Since If 2 test (12.53) is > 2 critical (5.99), We Reject H0.
The Conclusion: There is sufficient evidence at the 95% significance level to conclude that there is a relation between flavour preference and gender.
Observed Expected O-E (O-E)2 (O-E)2/E 416 400 16 256 0.64 419 400 19 361 0.9025 365 400 -35 1225 3.0625 4.605Related Questions
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