Explain how to use the sign test to test a population median.

Question

Accepted Answer

Hello there. Today we're gonna solve the following practice problem together. So first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. A researcher wants to test if the median of a population is equal to 45 using the sign test. Describe the steps to perform the sign test for this hypothesis. Awesome. So it appears for this particular problem we're asked to describe the steps that are required to perform a sign test for this particular hypothesis, which the hypothesis is that this researcher wants to test if the median of a population is equal to 45, once again using the sign test. So now that we know what we're ultimately trying to solve for, let's take a moment to read off our multiple choice answers to see what our final answer might be. A is state null hypothesis, count above and below 45. Ignore equals. Use smaller count as statistic. Use binomial with p equals 0.5. Compute p value compared to alpha. B is calculate mean compared to 45, U T distribution, compute p value compared to alpha. See is state null hypothesis. Count all data. Use normal approximation, compute Z score, compare to critical value. And finally, D is state null hypothesis. Use paired differences, calculate variance, use F test compared to alpha. Awesome. So our first step in order to solve this particular problem is we need to state our null hypothesis, which we will denote as H0 or H subscript 0, and the null hypothesis states that the median. is equal to 45. Fantastic. So moving right along here, our second step now is for each observation, as we should recall, we need to record if it is above, below, or equal to 45, and we need to ignore those that are equal to 45. Our third step is we need to count the number above, so Nubscript positive and below and negative 45. Our fourth step is we need to perform the test statistic is min. So let's make a note of this. So this is min parenthesis N positive, negative. As we stated in part three, so N positive and N negative. Fantastic. So our 5th step now. we need to note that and recall that under the null hypothesis, the number of signs follows a binomial distribution with N equaling N plus N negative and P is equal to 0.5. Fantastic. So now our sixth step is we need to calculate the P value for the observed statistic. And our 7th step is we need to compare the p value to alpha, where alpha denotes the level of significance, to decide whether or not we need to reject the null hypothesis. So that will be looking at our multiple choice answers. The correct answer, without a doubt, will have to be multiple choice answer letter A. Which once again states state the null hypothesis, so state null hypothesis, count above, below 45, ignore equals, use smaller count as statistic. Use binomial with P equals 0.5, compute p value and compare to alpha, and that's it. We've officially solved for this problem. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

Explain how to use the sign test to test a population median.

Key Concepts

Sign Test

Hypothesis Testing

Median

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