Annual growth rates for individual firms in the toy industry tend to fluctuate dramatically, depending on consumers'; tastes and current fads. Consider the following growth rates (in percent) for two companies in this industry, Hasbro and Mattel. Which of the following is the correct conclusion? A) Do not reject Η₀. We can conclude the growth rate variance of Hasbro is different from the growth rate variance of Mattel. B) Reject Η₀. We can conclude the growth rate variance of Hasbro is different from the growth rate variance of Mattel. C) Do not reject Η₀. We cannot conclude the growth rate variance of Hasbro is different from the growth rate variance of Mattel. D) Reject Η₀. We cannot conclude the growth rate variance of Hasbro is different from the growth rate variance of Mattel.

Question

Quizplus · Accepted Answer

We use a two-sample t-test to compare the variances of the growth rates of Hasbro and Mattel. The null hypothesis is that the variances are equal, and the alternative hypothesis is that they are different. The test statistic is calculated as F = s1^2/s2^2, where s1^2 is the sample variance of Hasbro and s2^2 is the sample variance of Mattel. The degrees of freedom for the test are calculated as df1 = n1 - 1 and df2 = n2 - 1, where n1 and n2 are the sample sizes for Hasbro and Mattel, respectively. Using the data provided in the table, we find that F = 30.46, df1 = 19, and df2 = 19. The critical value for the F-distribution with 19 and 19 degrees of freedom at the 5% level of significance is 2.15. Since F > 2.15, we cannot reject the null hypothesis. Therefore, we cannot conclude that the growth rate variance of Hasbro is different from the growth rate variance of Mattel. Thus, the correct answer is C: Do not reject Η₀. We cannot conclude the growth rate variance of Hasbro is different from the growth rate variance of Mattel.

Annual Growth Rates for Individual Firms in the Toy Industry