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for Class Work Questions pula PRACTICE PROBLEMS AT 72 cor Man and B. 1. Define the following terms A Null hypothesis B. Alternative hypothesis C. Test statistic D. Type I error E. Type II error F. Power of a test G. Rejection point (critical value). 2. Suppose that, on the basis of a sample, we want to test the hypothesis that the mean debt-to-total-assets ratio of companies that become takeover targets is the same as the mean debt-to-total-assets ratio of companies in the same industry that do not become takeover targets. Explain under what conditions we would commit a Type 1 enor and under what conditions we would commit a Type II error. 3. Suppose we are testing a null hypothesis, H, versus an alternative hypothesis, H. and the p-value for the test statistic is 0.031. Ar which of the following levels of significance-a = 0.10, a = 0.05, and/or a = 0,01 would we reject the null hypothesis? 4. Identify the appropriate test statistic or statistics for conducting the following hypothesis tests. (Clearly identify the test statistic and, if applicable, the number of degrees of freedom. For example, "We conduct the test using an x-statistic with y degrees of freedom.") A. HE - versus H * 0, where he is the mean of a normally distributed population with unknown variance. The test is based on a sample of 15 observations B. Hversus H:40, where is the mean of a normally distributed population with unknown variance. The test is based on a sample of 40 observations C. Hps versus H: > 0, where is the mean of a normally distributed population with known variance o' The sample size is 45 D. Ho - 200 versus : +200, where is the variance of a normally distributed population. The sample size is 50. C D. Th E. 10:21 22versustia 21.022 Hversus, where al 2 2 9. is the variance of a second is the variance of one normally distributed population and 622 normally distributed population. The test is based on two independent random samples. F. Ho (Population mean 1) - (Population mean 2) - versus H (Population mean 1) - (Population mean 2) * 0, where the samples are drawn from normally distributed populations with unknown variances. The observations in the two samples are correlated. G. Ho: Population mean 1) - Population mean 2) - versus He: (Population mean 1) - (Population mean 2) #0, where the samples are drawn from normally distributed populations with unknown but assumed equal variances. The observations in the two samples of size 25 and 30, respectively) are independent $. For each of the following hypothesis tests concerning the lation mean, , state the rejection point condition or conditions for the test statistic leg.11.25), denotes sample size. A. H=10 versus H, 10, using a t-test with n - 26 and a = 0.05 B. H=10 versus H #10, using a t-test with = 40 and e=0.01 C. Hus 10 versus Hu> 10, using a t-test with n = 40 and a = 0.01 D. HER 10 versus Hu> 10, using a M-test with n=21 and a = 0.05 E. H 10 versas
