# 7.10 Skills Focus: Selecting, Implementing, and Communicating Inference Procedures

#statisticalinference

#confidenceintervals

#significancetests

written by josh argo image courtesy of: pixabay.com

## Multiple Choice

When given a multiple choice question regarding inferential procedures, it is almost always going to pertain to selecting the correct procedure, interpreting a p-value or drawing a conclusion given a p-value.

### Selecting Correct Procedure

When asked to select a correct procedure, the best way of approaching the problem is to ask yourself 2 questions:

1. Am I dealing with means or proportions?

2. Do I have 1 or 2 samples?

This will help you to determine if you are running a 1/2 sample/prop t/z test/interval.

Those 2 questions are the guiding factor in answering what type of test/interval we will run.

Some special cases to note: when given one sample in an experimental study where every unit receives both treatments, this is a matched pairs t-test, not a 2 sample t test. Also, when dealing with multiple proportions (more than 2), a chi-square test may be necessary.

### Interpreting P-Value

When asked to interpret a p-value, remember that it is the probability of obtaining your given sample from the sampling distribution of that particular sample size, given that the true mean/proportion is what the null hypothesis claims.

Example

In a hypothesis test where the Ho: p=0.2 and the Ha: p<0.2, we collect a sample of 100 where our p-hat is 0.15. Our significance test reveals a p-value of 0.11. Interpret this p-value.

A p value of 0.11 tells us that the probability of obtaining a sample of 100 where the success rate was 0.15 or lower would happen approximately 11% of the time, given our normal sampling distribution when n=100.

### Drawing Conclusion

In drawing a conclusion from an inference procedure, we are generally comparing a p-value to a significance level. You can follow the chart below in making your decision:

 palpha: Fail to Reject the Ho We do not have significant evidence of the Ha (in context).

We never accept a Ho or Ha!

## Free Response

When dealing with free response questions requiring inferential procedures, we usually see one of the following 2 prompts:

1. Do the data give convincing evidence... (Significance Test)

2. Construct and interpret a ___% confidence interval (Confidence Interval)

Both of these stems can follow the SPDC Template outlined below:

### State the Parameters/Hypotheses

• When performing a confidence interval, here is where you should state what the parameter(s) are for our population(s) that we are estimating.

• When performing a significance test, this is the place in the problem when you should write the hypotheses for your questions. Also, label and identify your parameters.

• Remember, your Ho will always have an equal sign and your Ha will always have some form of inequality (<, > or not equal to)

### Plan the Problem

• This is where we check our three conditions for inference: Random, Independent and Normal. This is basically the same from confidence interval or significance test, but varies based on the type of data (categorical or quantitative).

### Do the Math

• Start out by identifying the test/interval you are performing. This is usually which function you are selecting in the STATS menu of your calculator. Write this down!

• Confidence Intervals: Just the interval is sufficient

• Significance Test: Critical Value, p-value, and df (if necessary)

### Conclusion

• This is where you follow templates given throughout the unit.

• For confidence intervals: "I am ___% confident that the true _____ of __________ is between (__, __).

• For significance tests: "Since the p(</>) alpha, I (fail to reject/reject) the Ho. There (is/is not) convincing evidence of Ha (in context of problem)."

🎥Watch: AP Stats - Review of Inference: z and t Procedures