Question

1. Target parameter. How do I know if the sample size is small or large?

2. How to set up H0 and Ha and how to recognize if the test is one-tailed or two tailed?

3. How to calculate the sample test statistics?

4. How to define rejection region?

Answer 1

1. Target parameter. How do I know if the sample size is small or large?

We see if the sample is greater than 30 or not.

If n > 30 , we can say that the sample size is large. It is mostly used as good approximation for normal distributions if we were to use t-distribution.

2. How to set up H0 and Ha and how to recognize if the test is one-tailed or two tailed?

Null hypothesis means that any relationship between the variables or any value of a parameter might be due to chance that there is no significance with some probability.

Alternative hypothesis means that any relationship between the variables or any value of a parameter is not merely due to chance that there is significance with some probability.

Null hypothesis and alternative are exactly opposites. What we have to test is usually the alternative hypothesis.We can read in the question

Eg. Check whether the population mean is greater than a specified value say 45 or not.

Null : The mean is equal to or less than 45

Alternative The mean is greater than 45.

The null hypothesis always has the equality sign.

To identify if it is

directional (one tailed): we see whether we are checking for greater or less than

2 -tailed: we are checking if it is equal to.

3. How to calculate the sample test statistics?

Test Statistic is usually different for different parameters.

Different parameters are calculated based on the different distributions.

Means have t-test and z-test, variance use chi-square test, More than 2 means use ANOVA (F-test),

4. How to define rejection region?

The rejection region is defined as the region where if the test statistic lies we reject the null hypothesis.

It is also different for different distribution. We calculate using the critical value or the p-value.