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# Constructing hypotheses for a significance test about a proportion

AP.STATS:
VAR‑6 (EU)
,
VAR‑6.D (LO)
,
VAR‑6.D.1 (EK)
,
VAR‑6.D.2 (EK)
,
VAR‑6.D.3 (EK)
,
VAR‑6.D.4 (EK)
,
VAR‑6.D.5 (EK)

## Video transcript

we're told that Amanda read a report saying that 49% of teachers in the United States were members of a labor union she wants to test whether this holds true for teachers in her state so she is going to take a random sample of these teachers and see what percent of them are members of a union let P represent the proportion of teachers in her state that are members of a union write an appropriate set of hypotheses for her significance test so pause this video and see if you can do that I know let's do it together so what we want to do for this significance test is set up a null hypothesis and an alternative hypothesis now your null hypothesis is the hypothesis that hey there's no news here it's what you would expect it to be and so if you read a report saying that forty-nine percent of teachers in the United States were members of labor unions well then it would be reasonable say that the the null hypothesis the no news here is that the same percentage of teachers in their state are members of elute labor union so that percentage that proportion is P so this would be the null hypothesis that the proportion in her state is also 49 percent and now what would the alternative be well the alternative is that the proportion in her state is not forty-nine percent this is the thing that hey there would be news here there'd be something interesting to report there's something different about her state and how would she use this well she would take a sample of teachers in her state figure out the sample proportion figure out the probability of getting that sample proportion if we were to assume that the null hypothesis is true if that probability is lower than a threshold where she should have said ahead of time her significance level then she would reject the null hypothesis which would suggest the alternative most - another example here according to a very large poll in 2015 about 90% of homes in California had access to the Internet market researchers want to test if that proportion is now higher so they take a random sample of 1,000 homes in fornia and find that 920 or 92% of homes sampled have access to the Internet let P represent the proportion of homes in California that have access to the Internet write an appropriate set of hypotheses for their significance test so once again pause this video and see if you can figure it out so once again we want to have a null hypothesis and we want to have an alternative hypothesis the null hypothesis is the hey there's no news here and so that would say that there's kind of status quo that the proportion of people who have internet is still the same as the last study is still the same at 90% or I could write 90% or I could write zero point I could write 0.9 right over here now some of you might have been tempted to put 92 percent in there but it's very important to realize 92% is the sample proportion that's the sample statistic when we're writing these hypotheses this is about these are hypotheses about the true parameter what is the proportion of the true proportion of homes in California that now have the Internet and so this is about the true proportion and so the alternative here is that it's now greater than 90 percent or I could say it's greater than 0.9 I could've written 90 percent or 0.9 here and so they really in this question they wrote this to kind of distract you to make you think oh maybe I have to incorporate this in 92 percent somehow and once again how will they use these hypotheses well they will take this sample in which they got 92 percent of homes samples had access to the Internet so this right over here is my sample proportion and then they're going to figure out well what's the probability of getting this sample proportion for this sample size if we were to assume that the null hypothesis is true if this probability of getting this is below a thresholds below alpha below our significance level then we'll reject the null hypothesis which would suggest to the alternative