EXERCISES For Exercises 13 through 2 15, assume the sample populations do not have equal standard deviations and use the .05 significance level: (a) Determine the number of degrees of freedom and round down to the nearest integer value, (b) state the decision rule, (c) compute the value of the test statistic, and (d) state your decision about the null hypothesis. 13. The null and alternate hypotheses are: Ho : H1 = H2 HI:HI # HZ A random sample of 15 items from the first population showed a mean of 50 and a standard deviation of 5. A sample of 12 items for the second population showed a mean of 46 and a standard deviation of 15. 14. The null and alternate hypotheses are: Ho : HI - H2 H1 : HI > H2 A random sample of 20 items from the first population showed a mean of 100 and a standard deviation of 15. A sample of 16 items for the second population showed a mean of 94 and a standard deviation of 8. Use the .05 significance level. 15. A recent survey compared the costs of adoption through public and private agencies. For a sample of 16 adoptions through a public agency, the mean cost was $21,045, with a standard deviation of $835. For a sample of 18 adoptions through a private agency, the mean cost was $22,840, with a standard deviation of $1,545