Question

Suppose you are wondering if male and female have different opinions about the current president of US and you want to compare to see if there is a difference in terms of gender.

Your tasks:

(1) Phrase your null and alternative hypotheses

(2) Define your test statistics and the sampling distribution

(3) How you collect your sample,

(4) How you make a conclusion based on your sample

(5) Are there any factors that could invalidate your conclusion ? Try give one

Answer 1

1) Null hypothesis, H₀: Male and female have same opinions about current US president

Alternative hypothesis, H_a: Male and female have different opinions about current US president

2) Test statistics in this case would be the T-statistic and the test would be the independent samples T-test. Sampling distribution is normal distribution.

3) We collect the sample by collecting the opinions from males and females independently such that the readings are not paired.

4) If the value of the T-statistic is greater than the critical T-score derived on the basis of level of significance and degrees of freedom of the samples, we reject the null hypothesis, otherwise we cannot reject the null hypothesis at the given level of significance.

5) Our conclusion could be invalidated if the samples collected are not independent, for example if we have surveyed transgenders and classified them as male as well as female given we have only 2 categories. Independence of samples is necessary for this test.