Hypothesis Testing READ THIS: For hypothesis testing, we don't know the true population mean, but we do have a reasonable guess, possibly from previous research, which we call up- This number goes in the null hypothesis. The point of hypothesis testing is to see how the true population mean compares to this reasonable guess without having to take a full census. Since we don't know what the population mean really is, we use a simple random sample and calculate a sample statistic. However, we know that every time we take a sample, there is always random variability, so we need to take that into account when we estimate our population parameter. This is why you don't just compare the sample statistic directly to up. Instead, we need to see how unusual our sample statistic is if the null hypothesis is true. If the sample statistic isn't too many standard deviations away from Ho, then random chance could explain any discrepancy, and we have no reason to reject the null hypothesis. If the sample statistic is very far away from u., then we say that our results are just too weird or extreme to have occurred simply due to random variation alone, and there is something wrong with our null hypothesis. How weird is too weird? We use a cut-off point, called the significance level (o, usually 0.05). If the P-value is less than the significance level, meaning results as extreme as yours have a very small probability of occurring due to random chance, you reject the null hypothesis. 8. (8 points) Fill in the chart below for how we make decisions about conclusions to hypothesis tests. Your answer choices are in boldface type. P-value > P-value S of a) Is the sample mean X near or far from the reasonable guess for the population mean ly b) On the Normal curve diagram for this hypothesis test, does the p-value take up a small or big area? c) Conclusion to the hypothesis test: Reject Ho. Do not reject Ho d) There is or is not evidence in favor of the alternative hypothesis