The conclusion result in a correct decision.
The null hypothesis is that the mean is equal to 55. The alternative hypothesis is that the mean is less than 55. The significance level is 0.05. The test statistic is -1.51.
The p-value is the probability of getting a test statistic as extreme or more extreme than the one that was observed, assuming that the null hypothesis is true. In this case, the p-value is 0.0668.
Since the p-value is greater than the significance level, we fail to reject the null hypothesis. This means that we do not have enough evidence to conclude that the mean is less than 55.
If the true value of the mean is 52, then we have made a correct decision. This is because the true value of the mean is less than 55, and we did not reject the null hypothesis that the mean is equal to 55.
Therefore, the conclusion result in a correct decision.
Question
A test of H_(0):mu =55 versus H_(1):mu <55 is performed using a significance level of alpha =0.05. The value of the test statistic is z=-1.51.
If the true value of mu is 52 does the conclusion result in a Type I error, a Type II error, or a correct decision?