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: We will also frequently look at both P-values and confidence intervals to make sure the two methods align. There are generally 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. If this is above alpha, then she would fail to reject her 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: Then she would reject her null hypothesis, which Would compare this p value to her preset significance ![]() Our p value would be approximately 0.053. Our sample size is seven so our degrees of freedom would be six. And then our degrees of freedom, that's our sample size minus one. It's an approximation of negative infinity, very, very low number. It to be negative infinity and we can just call Would go to 2nd distribution and then I would use the t cumulative distribution function so let's go there, that's the number six I'm gonna do this with a TI-84, at least an emulator of a TI-84. Is more than 1.9 below the mean so this right What is the probability of getting a t value that Of the t distribution, what we are curious about,īecause our alternative hypothesis is that the T distribution really fast, and if this is the mean So, if we think about a t distribution, I'll try to hand draw a rough The way we get that approximation, we take our sample standard deviation and divide it by the square ![]() Is equal to her sample mean, minus the assumed meanįrom the null hypothesis, that's what we have over here, divided by and this is a mouthful, our approximation of the standard error of the mean. The way she would do that or if they didn't tell us ahead From that, she wouldĬalculate her sample mean and her sample standard deviation, and from that, she wouldĬalculate this t statistic. Miriam takes a sample, sample size is equal to seven. That the true mean is 18, the alternative is that it's less than 18. Some population here and the null hypothesis is To remind ourselves what's going on here before I go aheadĪnd calculate the p value. Value for Miriam's test? So, pause this video and see if you can figure this out on your own. Assume that the conditionsįor inference were met. Her test statistic, IĬan never say that right, was t is equal to negative 1.9. ![]() Testing her null hypothesis that the population mean of some data set is equal to 18 versus herĪlternative hypothesis is that the mean is less than 18 with a sample of seven observations.
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