Hypothesis Testing

Hypothesis testing on mean and means

In this chapter we inform the reader about the different means to calculate the hypothesis for mean and means with one sample t-test, two sample t-test and finally with the z-test. We also look into one-tailed and two-tailed and to the p-value. In the end there are step-by-step examples on how to conduct a calculation.

Hypothesis test for a mean

There are two different methods to use, one is the one-sample t test and the other the z-test

Small-sample test concerning mean. When we have a small sample for under 30 samples we conduct the one-sample t test.

Large-sample test concerning mean. When we have a large sample for over 30 samples we conduct the z-test.

Example for mean in a one-tailed test

Bon Air Elementary School has 300 students. The principal of the school thinks that the average IQ of students at Bon Air is at least 110. To prove her point, she administers an IQ test to 20 randomly selected students. Among the sampled students, the average IQ is 108 with a standard deviation of 10. Based on these results, should the principal accept or reject her original hypothesis? Assume a significance level of 0.01.

Solution: The solution to this problem takes four steps: (1) state the hypotheses, (2) formulate an analysis plan, (3) analyze sample data, and (4) interpret results. We work through those steps below:

* State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: μ >= 110 

Alternative hypothesis: μ < 110

Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the sample mean is too small.

* Formulate an analysis plan. For this analysis, the significance level is 0.01. The test method is a one-sample t-test.

* Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t-score test statistic (t).

SE = s / sqrt(n) = 10 / sqrt(20) = 10/4.472 =...