Question

When doing statistical inference, we check three broad classes of assumptions: (1) randomization, (2) independence, and (3) normality of the sampling distribution. What is the consequence of violating these assumptions?

1. (1) biased sample statistics, (2) invalid inference, (3) invalid inference
2. (1) invalid inference, (2) biased sample statistics, (3) invalid inference
3. (1) invalid inference, (2) invalid inference, (3) biased sample statistics
4. (1) biased sample statistics, (2) biased sample statistics, (3) invalid inference
5. (1) biased sample statistics, (2) invalid inference, (3) biased sample statistic

. Please choose the option that best complete the following sentence: When conducting a hypothesis test, we                                        and then evaluate the results from the test to determine if there is enough evidence to

1. Assume that the null hypothesis is true; reject the null hypothesis
2. Assume that the null hypothesis is false; accept the null hypothesis
3. Assume that the alternative hypothesis is true; reject the null hypothesis
4. Assume the alternative hypothesis is false; reject the alternative hypothesis

Answer 1

1) Option (a) (1) biased sample statistics, (2) invalid inference, (3) invalid inference

Justification: The assumption of randomization gives rise to the claim that every subject in the target population got an equal chance of being selected in the sample, the lack of which provides a bias in the sample statistics.

The independence assumption allows us to use simple statistical concepts to quantify the evidence for/against the null hypothesis. Lack of which leads to an invalid inference.

Also, the lack of normality assumption leads to an invalid inference.

2) Option (a) When conducting a hypothesis test, we assume that the null hypothesis is true, and then evaluate the results from the test to determine if there is enough evidence to reject the null hypothesis.

Justification: The basic structure of a hypothesis testing is to first consider that the null hypothesis is true, then we set up the level of significance, calculate the test statistics, find the critical region and then test the claim whether the null hypothesis is true or not, i.e. decide whether we are to accept or reject null hypothesis.