Question

Why is accepting the null hypothesis misleading?

Why do you think people commonly accept the null hypothesis?

How would you explain the meaning of P-value to someone who has not studied statistics?

When are two samples independent? Dependent?

How do the techniques of each of the following compare: a) testing a claim about two population proportions from two independent simple random samples (SRS), b) testing a claim about two population means from two independent SRS's, c)testing a claim about two population means from two dependent SRS's?

Why are the P-value method of hypothesis testing, the critical value method of hypothesis testing, and confidence intervals equivalent methods, in the sense that they result in the same conclusion?

Answer 1

Why is accepting the null hypothesis misleading?

Accepting null hypothesis is misleading because sometimes it happens that while doing an analysis we do not get sufficient evidence to disprove the null hypothesis and thus we may wrongly say that we are accepting the null hypothesis when in fact we donot have sufficient evidence to reject it.

Why do you think people commonly accept the null hypothesis?

As explained above people commonly accept null hypothesis because they do not have enough evidence to reject it.

How would you explain the meaning of P-value to someone who has not studied statistics?

P value is the probability of wrongly rejecting the null hypothesis.
It is the least signficant level at which you can accept the null hypothesis.
If the observed statistic happens to be just a chance, p-value tells us what is the probability of that chance.

When are two samples independent? Dependent?
Two samples are said to be independent if they are taken from a same or different population but they do not affect each other in any way possible.

Whereas a dependent sample means testing the same sample under different conditions.

How do the techniques of each of the following compare: a) testing a claim about two population proportions from two independent simple random samples (SRS), b) testing a claim about two population means from two independent SRS's, c)testing a claim about two population means from two dependent SRS's?
Two population proportions.
.

2 population means from independent sample
For 2 dependent samples:
A t-test for two paired samples is a hypothesis test that attempts to make a claim about the population means .

• 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)