#Xsection 10.2 free

The telephone poll of 602 likely Michigan voters was conducted Sept. The EPIC-MRA poll conducted for The Detroit News and television stations WXYZ, WILX, WOOD and WJRT found 50 percent of likely Michigan voters support the stem cell proposal, 32 percent against and 18 percent undecided. pollĪ recent poll shows voter support leading opposition for ballot proposals to loosen Michigan's restrictions on embryonic stem cell research and allow medical use of marijuana. Stem cell, marijuana proposals lead in Mich. This isn't something every statistics text will mention, nor will every instructor mention, but it's important.Ĭonsider the excerpt shown below (also used in Example 1, in Section 9.3) from a poll conducted by Pew Research: The problem is that it's relatively easy to get a large p-value - just get a really large sample size! So the chart above is really with the caveat ' assuming equal sample sizes in comparable studies. These values are not hard lines, of course, but they can give us a general idea of the strength of the evidence.īut wait! There is an important caveat here, which was mentioned earlier in the section about The Controversy Regarding Hypothesis Testing.

P-value ≥ 0.1: weak to no evidence supporting the alternative hypothesis.

0.05 ≤ P-value < 0.1: some evidence supporting the alternative hypothesis.

0.01 ≤ P-value < 0.05: strong evidence supporting the alternative hypothesis.

P-value < 0.01: very strong evidence supporting the alternative hypothesis.

The smaller the P-value, the stronger the evidence supporting the alternative hypothesis. Since the P-value represents the probability of observing our result or more extreme, the smaller the P-value, the more unusual our observation was. The reason why we do multiply by two is that even though the result was on one side, we didn't know before collecting the data, on which side it would be. It may seem odd to multiply the probability by two, since 'or more extreme' seems to imply the area in the tail only. In a two-tailed test, the P-value = 2P(Z > |z o|). Step 5 : Reject the null hypothesis if the P-value is less than the level of significance, α. ( α will often be given as part of a test or homework question, but this will not be the case in the outside world.) Step 2 : Decide on a level of significance, α, depending on the seriousness of making a Type I error. As usual, the following two conditions must be true: In this first section, we assume we are testing some claim about the population proportion. Testing Claims Regarding the Population Proportion Using P-Values So what we do is create a test statistic based on our sample, and then use a table or technology to find the probability of what we observed. So is observing 74% of our sample unusual? How do we know - we need the distribution of !

You might recall that based on data from, 68.5% of ECC students in general are par-time. Why are these important? Well, suppose we take a sample of 100 online students, and find that 74 of them are part-time.

The standard deviation of the sampling distribution of is.

The mean of the sampling distribution of is.

The shape of the sampling distribution of is approximately normal provided.

In Section 8.2, we learned about the distribution of the sample proportion, so let's do a quick review of that now.įor a random sample of size n such that n≤0.05N (in other words, the sample is less than 5% of the population), The P-value is the probability of observing a sample statistic as extreme or more extreme than the one observed in the sample assuming that the null hypothesis is true. In general, we define the P-value this way:

#Xsection 10.2 free

If you're interested in learning any of these other methods,įeel free to read through the textbook.

Your textbook references three different methods for testing hypotheses:īecause P-values are so much more widely used, we willīe focusing on this method. In other words, the observed results are so unusual, that our original assumption in the null hypothesis must not have been correct. If the observed results are unlikely assuming that the null hypothesis is true, we say the result is statistically significant, and we reject the null hypothesis. Once we have our null and alternative hypotheses chosen, and our sample data collected, how do we choose whether or not to reject the null hypothesis? In a nutshell, it's this: