How to Support or Reject a Null Hypothesis (for a Proportion)

critical values and z-tables, Hypothesis testing 8 Comments

Sometimes, you’ll be given a proportion of the population or a percentage and asked to reject or support the researcher’s claim. In this case you can’t compute a test value by calculating a z-score (you need actual numbers for that), so we use a slightly different technique. If you have specific numbers instead of a proportion, check out this article on how to support/reject a null hypothesis.

Sample question: A researcher claims that 16% of vegetarians are actually vegans. In a recent survey, 19 out of 100 vegetarians stated they were vegan. Is there enough evidence at α=0.05 to support this claim?

Step 1: State the null hypothesis and the alternate hypothesis (“the claim”). Ho:p=0.16 (claim); H1:p≠0.16

If you aren’t sure how to do this, follow this link for How To State the Null and Alternate Hypothesis.

Step 2: Find the critical value.
Here is a how-to on finding the critical value for a left-tailed test as a reminder. You may need to find a right-tailed or two-tailed instead.

Step 3: Compute phat by dividing the number of positive respondents from the number in the random sample:
19/100 = 0.19.

Step 4:Find ‘p’ by converting the stated claim to a decimal:
16%=0.16.
Also, find ‘q’ by subtracting from 1: 1-0.16=0.84.

Step 5: Use the following formula to calculate your test value.

NULL HYPOTHESIS test value with a proportion

Click here if you want easy, step-by-step instructions for solving this formula.

If formulas confuse you, this is asking you to:

  1. Subtract p fromphat(0.19-0.16=0.03). Set this number aside.
  2. Multiply p and q together, then divide by the number in the random sample. (0.16 x 0.84) / 200 = 0.000672
  3. Take the square root of your answer to 2. sqrt(0.000672)=0.0259
  4. Divide your answer to 1. by your answer in 3. 0.03/0.0259=1.158.

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Step 6: Compare your answer from step 5 with the α value given in the question. If step 5 is less than α, reject the null hypothesis, otherwise do not reject it. In this case, 1.158 is not less than our α, so we do not reject the null hypothesis.

Related posts:

  1. How to Support or Reject a Null Hypothesis (for a Proportion: P-Value Method)
  2. How to Support or Reject a Null Hypothesis (Using a P-Value)
  3. How to Support or Reject a Null Hypothesis
  4. How to State the Null Hypothesis in Statistics: Part Two
  5. How to State the Null Hypothesis in Statistics: Part One
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8 Responses to “How to Support or Reject a Null Hypothesis (for a Proportion)”

  1. Angie Widdows said:

    Oct 23, 09 at 9:53 am

    I think my problem with these types of questions is that I cannot seem to get past the first step (Ho:p=0.16 (claim); H1:p≠0.16) I looked at the link on how to get this but I still am very confused. After that first step, I can figure out the rest although I am not sure why what is being done is being done.

  2. Stephanie said:

    Oct 23, 09 at 10:52 am

    Angie,
    Can you elaborate on what part is confusing?
    For example, is it the terminology (Ho, p=) that is getting you stuck, or is it deciding which part is the null hypothesis?
    Stephanie

  3. Mary Johnson said:

    Oct 27, 09 at 4:12 pm

    Thanks for putting that “finding the critical value” link on this. I needed it. It did help when I figured out where some of the numbers were coming from.

  4. Lauren Schultz said:

    Nov 02, 09 at 7:18 am

    THIS HAS BEEN MY DEMISE LOL… I CAN GET ALL THE WAY DOWN TO HAVING TO CHOSE YES OR NO, IN REGARDS TO SUPPORT/REJECT. I DO NOT KNOW HOW TO FIGURE IT OUT. SOLVING THE PROBLEM IS EASY BUT ANSWERING IT THROWS ME OFF..

  5. Donna Allen said:

    Nov 02, 09 at 2:52 pm

    I agree with Lauren. I completely get it when it comes to solving the mathematical part of the problem. But, I get stumped every time on yes or no as to whether reject or support the hypothesis. I can’t seem to get the hang of this.

  6. Angie WIddows said:

    Nov 29, 09 at 5:41 pm

    To answer your question on what I am confused on, yes and Yes. Both. I will be glad when Chapter 8 is over.

  7. Vanessa DuBarry said:

    Dec 14, 09 at 9:07 pm

    I have the same problem, I can solve this but then whether deciding yes or no is where I get stuck, This is the hardest deciding.

  8. crystal lydick said:

    Mar 27, 10 at 11:35 am

    I also am having a hard time with Chapter 8! But, the more I look at this website the more it helps explain things more clearly! I just have to read the info over and over and then I have that moment where I finally get it!

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