Please indicate either TRUE or FALSE for the questions. If you indicate FALSE as your answer, briefly explain why the statement is false.
1. In order to compare the characteristics of two different populations, a sample should be extracted from each population.
2. When two populations are compared and samples taken from each, the data derived from the second sample should be dependent on the data from the first sample.
3. Whenever two population means are being compared, an acceptable null hypothesis is that the two population means equal each other.
4. Whenever two population means equal each other, the difference between them must be zero.
5. Irrespective of whether a two-tail or one-tail test is being conducted in order to compare two population means, the larger the differences in the sample means, the more likely that the null hypothesis will be rejected.
6. A large-sample test for the difference between two populations can be conducted safely provided either of the two samples exceeds 30.
7. The recommended procedure for estimating the pooled variance is to combine all the data from both samples together and calculate the variance as if it were one sample.
8. If two samples both have less than 30 observations and unknown variances, there is no statistical test that can be used to compare the population means, even if both populations are normally distributed.
9. Given a paired study with 14 pretreatment measures and 14 post-treatment measures, the number of degrees of freedom for the test statistic is 28 - 1 = 27.
10. The null hypothesis for the difference between two population variances is the same for both two-sided, lower-tail, and upper-tail tests.
The solution provides step by step method for the calculation of test statistic and p value. Formula for the calculation and Interpretations of the results are also included.