Question

1. In testing H0 : ?1 ? ?2 = 0 versus Ha : ?1 ? ?2 ? 0, the computed value of the test statistic is z = 1.99. The p-value for the two-tailed test is then . 2. The degrees of freedom associated with the pooled t test, based on sample sizes m and n, is given by . 3. Provided that at least one of the sample sizes m and n of two independent samples X and Y is small, and that the corresponding populations are both normally distributed with unknown values of the population variances, then a confidence interval for the difference between the two population means ?1 ? ?2, with a confidence level of 100(1 ? ?)% is . 4. The rejection region for level 0.05 paired t test in testing H0 : ?D ? 0 versus Ha : ?D > 0 is , where the data consists of 24 independent pairs. 5. In testing H0 : ?D = 0 versus Ha : ?D ? 0 where ?D is the true mean difference in paired data consisting of 23 independent pairs, the value of the test statistic is found to be 2.30. Then the p-value is between and . 6. If X?1 and X?2 are independent random variables with ?1 and ?2 degrees of freedom respectively, then the random variable F = (X?1/?1)/(X?2/?2) has an F distribution. 7. Let X1,…,X9 be a random sample from a normal distribution with variance ?1^2, and let Y1,…,Y12 be another random sample (independent of the Xi's) from a normal distribution with variance ?2^2, and let s1^2 and s2^2 denote the two sample variances. Then the random variable has an F distribution F = (s1^2/?1^2)/(s2^2/?2^2) with ?1 = and ?2 = . 8. Two independent samples of sizes m and n and variances s1^2 and s2^2 are selected at random from two normal distributions with variances ?1^2 and ?2^2. In testing H0 : ?1^2 = ?2^2 versus Ha : ?1^2 ? ?2^2, where the test statistic value is f = s1^2/s2^2 the rejection region for a level 0.05 test is either f ? or f < __.

          1. In testing H0 : ?1 ? ?2 = 0 versus Ha : ?1 ? ?2 ? 0, the computed value of the test statistic is z = 1.99. The p-value for the two-tailed test is then __________.

2. The degrees of freedom associated with the pooled t test, based on sample sizes m and n, is given by __________.

3. Provided that at least one of the sample sizes m and n of two independent samples X and Y is small, and that the corresponding populations are both normally distributed with unknown values of the population variances, then a confidence interval for the difference between the two population means ?1 ? ?2, with a confidence level of 100(1 ? ?)% is __________.

4. The rejection region for level 0.05 paired t test in testing H0 : ?D ? 0 versus Ha : ?D > 0 is __________, where the data consists of 24 independent pairs.

5. In testing H0 : ?D = 0 versus Ha : ?D ? 0 where ?D is the true mean difference in paired data consisting of 23 independent pairs, the value of the test statistic is found to be 2.30. Then the p-value is between __________ and __________.

6. If X?1 and X?2 are independent __________ random variables with ?1 and ?2 degrees of freedom respectively, then the random variable F = (X?1/?1)/(X?2/?2) has an F distribution.

7. Let X1,…,X9 be a random sample from a normal distribution with variance ?1^2, and let Y1,…,Y12 be another random sample (independent of the Xi's) from a normal distribution with variance ?2^2, and let s1^2 and s2^2 denote the two sample variances. Then the random variable has an F distribution F = (s1^2/?1^2)/(s2^2/?2^2) with ?1 = __________ and ?2 = __________.

8. Two independent samples of sizes m and n and variances s1^2 and s2^2 are selected at random from two normal distributions with variances ?1^2 and ?2^2. In testing H0 : ?1^2 = ?2^2 versus Ha : ?1^2 ? ?2^2, where the test statistic value is f = s1^2/s2^2 the rejection region for a level 0.05 test is either f ? __________ or f < __________.

1. In testing H0 : ?1 ? ?2 = 0 versus Ha : ?1 ? ?2 ? 0, the computed value of the test statistic is z = 1.99. The p-value for the two-tailed test is then .

2. The degrees of freedom associated with the pooled t test, based on sample sizes m and n, is given by .

3. Provided that at least one of the sample sizes m and n of two independent samples X and Y is small, and that the corresponding populations are both normally distributed with unknown values of the population variances, then a confidence interval for the difference between the two population means ?1 ? ?2, with a confidence level of 100(1 ? ?)% is .

4. The rejection region for level 0.05 paired t test in testing H0 : ?D ? 0 versus Ha : ?D > 0 is , where the data consists of 24 independent pairs.

5. In testing H0 : ?D = 0 versus Ha : ?D ? 0 where ?D is the true mean difference in paired data consisting of 23 independent pairs, the value of the test statistic is found to be 2.30. Then the p-value is between and .

6. If X?1 and X?2 are independent random variables with ?1 and ?2 degrees of freedom respectively, then the random variable F = (X?1/?1)/(X?2/?2) has an F distribution.

7. Let X1,…,X9 be a random sample from a normal distribution with variance ?1^2, and let Y1,…,Y12 be another random sample (independent of the Xi's) from a normal distribution with variance ?2^2, and let s1^2 and s2^2 denote the two sample variances. Then the random variable has an F distribution F = (s1^2/?1^2)/(s2^2/?2^2) with ?1 = and ?2 = .

8. Two independent samples of sizes m and n and variances s1^2 and s2^2 are selected at random from two normal distributions with variances ?1^2 and ?2^2. In testing H0 : ?1^2 = ?2^2 versus Ha : ?1^2 ? ?2^2, where the test statistic value is f = s1^2/s2^2 the rejection region for a level 0.05 test is either f ? or f < .

Added by Amy H.

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