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The alternative hypothesis is that the mean is not m. In this example:'Cannot Reject the Null Hypothesis because p > 0.05 (Means are the Same/Means are not Different). h ztest(x,m,sigma) returns a test decision for the null hypothesis that the data in the vector x comes from a normal distribution with mean m and a standard deviation sigma, using the z-test. Mathematically first we decide the null hypothesis and calculate the Z score for the distribution using the formula. QI Macros compares the p-value (0.192) to the significance level (0.05) and interprets the result for you. In this case, the \(p\)-value is \(P(Z<-1.75)=0.0401\):Īs expected, we reject the null hypothesis because the \(p\)-value \(=0.0401<\alpha=0.05\). Q Macros will perform the z test calculations AND interpret the results for you: Interpreting the z test Results. Recall that the \(p\)-value approach tells us to reject the null hypothesis at the \(\alpha=0.05\) level if the \(p\)-value \(\le \alpha=0.05\). p0 (hypothesized population proportion) p (observed sample proportion) n (sample size) z-statistic: 0.55487. Therefore, we reject the null hypothesis because \(Z=-1.75<-1.645\), and therefore falls in the rejection region:Īs always, we draw the same conclusion by using the \(p\)-value approach. To perform a one proportion z-test, simply fill in the information below and then click the Calculate button. Imagine you are consulting a university and want to carry out an analysis on how students are performing on average. The critical region approach tells us to reject the null hypothesis at the \(\alpha=0.05\) level if \(Z<-1.645\). Hypothesis Testing: Performing a Z-Test Now that we have an idea about the significance level, let’s get to the mechanics of hypothesis testing. The null hypothesis is \(H_0:\mu=85\), and the alternative hypothesis is \(H_A:\mu\mu_0\).įor the example in hand, the value of the test statistic is: