Question

1) What is a hypothesis, a hypothesis test, a null hypothesis and an alternative hypothesis?

2) What is a P-value, critical value and a test statistic? Provide an example of each and describe how they are used to test claims.

3) When conducting a hypothesis test, what is the difference between the P-value method and the critical-value method?

4) List and explain all the steps for performing a hypothesis test.

Directions: write the finding of these questions in a short passage around 200-300 words

Answer 1

A hypothesis is an educated guess about something in the world around you. It should be testable, either by experiment or observation. For example:

• A new medicine you think might work.
• A way of teaching you think might be better.

Hypothesis testing in statistics is a way for you to test the results of a survey or experiment to see if you have meaningful results. You’re basically testing whether your results are valid by figuring out the odds that your results have happened by chance.

Null hypothesis is always the accepted fact. Simple examples of null hypotheses that are generally accepted as being true are:

1. DNA is shaped like a double helix.

A null hypothesis is a hypothesis that says there is no statistical significance between the two variables. An alternative hypthesis is one that states there is signifanct relationship between two variables

2-

A test statistic is a random variable that is calculated from sample data and used in a hypothesis test. You can use test statistics to determine whether to reject the null hypothesis. The test statistic compares your data with what is expected under the null hypothesis.

A critical value is a point (or points) on the scale of the test statistic beyond which we reject the null hypothesis, and, is derived from the level of significance α of the test.

As we know critical value is a point beyond which we reject the null hypothesis. P-value on the other hand is defined as the probability to the right of respective statistic (Z, T or chi). The benefit of using p-value is that it calculates a probability estimate, we can test at any desired level of significance by comparing this probability directly with the significance level.

For e.g., assume Z-value for a particular experiment comes out to be 1.67 which is greater than the critical value at 5% which is 1.64. Now to check for a different significance level of 1% a new critical value is to be calculated.

However, if we calculate p-value for 1.67 it comes to be 0.047. We can use this p-value to reject the hypothesis at 5% significance level since 0.047 < 0.05

3- The critical value approach and the P-value approach give the same results when testing hypotheses. The P-value approach has the advantage in that you just need to compute one value, the P-value, to do the test. For the critical value approach, you need to compute the test statistic and find the critical value corresponding to the given confidence or significance level.

The critical value is the standard score such that the area in the tail on the opposite side of the critical value (or values) from zero equals the corresponding significance level, α . The P-value is the probability of obtaining a test statistic as extreme as the one for the current sample under the assumption that the null hypothesis is true.

4-

The following steps are involved in hypothesis testing:

The first step is to state the null and alternative hypothesis clearly. The null and alternative hypothesis in hypothesis testing can be a one tailed or two tailed test.

The second step is to determine the test size. This means that the researcher decides whether a test should be one tailed or two tailed to get the right critical value and the rejection region.

The third step is to compute the test statistic and the probability value. This step of the hypothesis testing also involves the construction of the confidence interval depending upon the testing approach.

The fourth step involves the decision making step. This step of hypothesis testing helps the researcher reject or accept the null hypothesis by making comparisons between the subjective criterion from the second step and the objective test statistic or the probability value from the third step.

The fifth step is to draw a conclusion about the data and interpret the results obtained from the data.