Question

we have a variety of options when choosing a test or a confidence interval. I'd like for you to walk us through your process of choosing based on what you see in the problem. What do you look for? What helps you decide what to choose?

Answer 1

1) Every information based on past experience is belongs to null hypothesis. But sometimes, question provide some claims  which is alternative hypothesis. Claims are always a new pattern which are different from past trend . so past trend is null hypothesis and OPPOSITE of past trend is some claim given to the question which ultimately becomes alternative hypothesis.

Hence most of the time , question gives you a some claims of statement such as "the salary of man is greater than that of female" which is alternative hypothesis . but question doesn't mention about the null hypothesis. so the opposite of claims statement becomes null hypothesis . Like for the above example : the salary of man is equal or less than that of female. Mostly we write null hypothesis in the form of equal sign only . so the null hypothesis is " salary of man and women is equal".

2) If the question is asked for the average amount and the population standard  deviation is given then we use the test statistics which follow the normal distribution. If population standard  deviation is not given , we estimate it by sample deviation and the we replace the by S (Sample standard deviation) . and the given test statistics follow t-distribution.

(I) here, if population standard deviation is given,

follows N(0,1)

(II) and, if population standard deviation is not given,

follow the distribution.

(1-) %confidence interval for population average if population standard deviation is given, is given by

(bar)

and (1-) %confidence interval for population average if population standard deviation is not given, is given by

(bar)