Now we can look up the probability: P z < − 0.471 on a probability table. Since 0.3192 is greater than P = 0.05, we cannot reject the null hypothesis that the sample mean is significantly different than the metal disc population mean.Įnter values for the population mean, population standard deviation, sample size and sample mean in order to compute the z-value. We will assume a significance level of α = 0.05. When you calculate the \(p\)-value and draw the picture, the \(p\)-value is the area in the left tail, the right tail, or split evenly between the two tails.If no level of significance is given, a common standard to use is \(\alpha = 0.05\).The statistician setting up the hypothesis test selects the value of α to use before collecting the sample data.In a hypothesis test problem, you may see words such as "the level of significance is 1%." The "1%" is the preconceived or preset \(\alpha\).If the z-value is less than the left critical value or greater than the right critical value, there is evidence to reject the null hypothesis that sample mean follows the same distribution as the population. The alternative hypothesis, \(H_\) is very close to alpha.For this reason, we call the hypothesis test left, right, or two tailed. In reality, one would probably do more tests by giving the dog another bath after the fleas have had a chance to return. In a study of 420,019 cell phone users, 172 of the subjects developed brain cancer. Test the claim that cell phone users developed brain cancer at a greater rate than that for non-cell phone users (the rate of brain cancer for non-cell phone users is 0.0340%). Since this is a critical issue, use a 0.005 significance level. You can determine a precise p-value using the calculator above, but we can find an estimate of the p-value manually by calculating the z-score as follows: z (p 1 - p 2 - D) / SE.Explain why the significance level should be so low in terms of a Type I error. We need to conduct a hypothesis test on the claimed cancer rate. The z-score is a test statistic that tells us how far our observation is from the difference in proportions given by the null hypothesis under the null distribution.