## Statistics Math Tutoring

There are common questions that students have in statistics. We answer a couple here and are willing to answer others for you. Click on the "Contact Us" tab above. ?The list below has the topics for questions students ask:

Hypothesis Testing (P-value Method)

**PERMUTATIONS OR COMBINATIONS? WHICH IS IT? **

Ian poses the question, "How do I decide if I should use the formula for the number of permutations or the number of combination? For example, I had the following question in the homework: On a test, a student is to answer 10 out of 13 questions. How many ways can this be done?

Ian, that is a very good question. Simply stated, a permutation is an order, an arrangement. A combination is a set of objects, a collection of objects, without regard to order. "Order" becomes the operative word.

Thus, the number of permutations of 13 items taken 10 at a time means the number of orders of 10 items taken from 13 items. And the number of combinations of 13 items taken 10 at a time means the number of collections of 13 items we can form from 13 items.

In your example, the question is, does it matter which order the 10 questions are selected? If order does, we use the number of permutation. If order does not matter, we use the number of combinations. The example by itself is unclear if we are to determine the number of orders or the number of sets of 10 questions we are to determine.

Anna wants to know, "My calculator keeps giving me P-value everytime I do a statistic test. I do not know what that is. Please help me."

Anna, The P-value is the probability of getting the test (sample) statistic or even a more extreme value as representing the sample data if the null hypothesis is true. The statistic is in the direction of the alternate hypothesis if the null hypothesis is true. On the normal curve, the P-value is the area beyond the test statistic.

Noah notes, "I have question deciding which Z-score formula to use."

Noah, that is a very common question.

The following formula is used to gain information about an individual data value from a population:

**z = (x – μ) / (σ) This is the basic z-score formula.**

The following formula is used to gain information about a sample mean, called a sampling distribution:

**z = (x – μ) / (σ / √n) where the x used here is the sample mean.**

Eric asks, "Just what is a hypothesis and what is hypothesis testing? I am confused about what it is and why we do it."

Eric, thanks for asking. First, a hypothesis is a claim about a population parameter: the population proportion, the population mean, or the population standard deviation.

Then, hypotheses testing is a decision-making process for testing the claim on the population. The researcher defines the population, defines the hypotheses about the population, define the level of significance, select a sample from the population, conduct the test procedure. and make a conclusion.

**HYPOTHESIS TESTING (P-VALUE METHOD)**

Peter of Kalamazoo College says, "Can you simplify the procedure for hypothesis testing using the P-value method?"

Sure Peter. Let us just go through these steps:

Step 1:State the null and alternate hypotheses and identify the claim you are making.

Step 2:Calculate your test value (Z-value).

Step 3:Determine the P-value corresponding to the Step 2 test value.

Step 4:Make decision to reject or not reject null hypothesis.

Step 5:Summarize the results in relation to the claim.

Emma asks, "Are there good statistics videos?"

Emma, there are great statistics videos at Khan Academy. Click on http://www.khanacademy.org/. Then scroll down the page to the following topics:

Statistics: Videos for a first course in statistics.

Probability: Probability examples you will meet in your statistics class.

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