Consider the following 99% confidence interval: 0.537 < µd < 0.995 Which of the following is correct regarding this confidence interval? Group of answer choices The sample statistic of ̅d = 0.229 was used in the construction of this confidence interval. The sample sizes of both paired populations are necessarily equal. The confidence interval is indicating that there is a population mean difference between the two paired populations. b and c only
Consider the following 99% confidence interval:
0.537 < µd < 0.995
Which of the following is correct regarding this confidence interval?
The sample statistic of ̅d = 0.229 was used in the construction of this confidence interval.
The
The confidence interval is indicating that there is a population
- Paired t-test :
A t-test for two paired samples is a hypothesis test that attempts to make a claim about the population means ( and ). More specifically, a t-test uses sample information to assess how plausible it is for difference - to be equal to zero. The test has two non-overlapping hypotheses, the null and the alternative hypothesis. The null hypothesis is a statement about the population parameter which indicates no effect, and the alternative hypothesis is the complementary hypothesis to the null hypothesis.
- The main properties of the t-test for two paired samples are:
- The test required two dependent samples, which are actually paired or matched or we are dealing with repeated measures (measures taken from the same subjects)
- As with all hypotheses tests, depending on our knowledge about the "no effect" situation, the t-test can be two-tailed, left-tailed or right-tailed
- The main principle of hypothesis testing is that the null hypothesis is rejected if the test statistic obtained is sufficiently unlikely under the assumption that the null hypothesis is true
- The p-value is the probability of obtaining sample results as extreme or more extreme than the sample results obtained, under the assumption that the null hypothesis is true
- In a hypothesis tests there are two types of errors. Type I error occurs when we reject a true null hypothesis, and the Type II error occurs when we fail to reject a false null hypothesis
Null and Alternative Hypotheses for paired t-test :
The following null and alternative hypotheses need to be tested:
Ho: = 0
Ha: ≠ 0
This corresponds to a two-tailed test, for which a t-test for two paired samples be used.
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