In a study to see if profits were declining very much, a random sample of 23 companies was taken where profits were declining sharply and where the average return on assets for the previous three years had been 0.058 and the deviation typical sample of 0.055. In an independent random sample of 23 companies where profits were not declining significantly, the mean return had been 0.146 and the standard deviation 0.058 over the same period. Assume that the two population distributions are normal. and have the same standard deviations. a). Using a hypothesis test, check whether you should take the population variances to be equal. b). Test at the 5% level the null hypothesis that the population means of returns on assets are equal against the alternative hypothesis that the true mean is higher for firms where profits were not declining significantly.
In a study to see if profits were declining very much, a random sample of 23 companies was taken where profits were declining sharply and where the average return on assets for the previous three years had been 0.058 and the deviation typical sample of 0.055. In an independent random sample of 23 companies where profits were not declining significantly, the mean return had been 0.146 and the standard deviation 0.058 over the same period. Assume that the two population distributions are normal. and have the same standard deviations.
a). Using a hypothesis test, check whether you should take the population variances to be equal.
b). Test at the 5% level the null hypothesis that the population means of returns on assets are equal against the alternative hypothesis that the true mean is higher for firms where profits were not declining significantly.
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