Chapter 9
9.61 The null hypothesis represents the statement that a researcher is trying to disapprove of. It asserts that there is no statistical significance between variables. On the other hand, the alternative hypothesis is the inverse of the null hypothesis. It represents the statement that there is a statistical significance between the two variables.
9.62 In statistics, when the null hypothesis is rejected while it is true, the type one error occurs. It can be described as accepting the alternative hypothesis when the observed results are purely based on chance. A type II error happens when the null hypothesis is not rejected while it should be rejected since the alternative hypothesis is true.
9.63 The power of a test is defined as the probability of rejecting a false null hypothesis. In this case, the researcher makes the correct decision and avoids the type II error.
9.64 The relationship between two variables can take either direction. Thus, a one-tail test involves testing for the possibility of a relationship between two variables in one direction. On the contrary, a two-tail test investigates the relationship in two directions. In a one-tailed test, the alpha is used to test the significance in one direction. On the other side, the alpha is divided into two in a two-tail test, and each half used to test for the significance in both directions.
9.65 The p-value is described as the estimated likelihood of rejecting a true null hypothesis. It can also be stated as the probability that the calculated results will be as extreme as the observed results when the null hypothesis is true. It is the smallest point of significance where the null hypothesis is rejected. 9.66 Since the confidence interval provides a range of reasonable estimates of the population mean, it helps in making conclusions whether the sample mean would be equal to the population mean. The null hypothesis that the sample mean is not equal to the population mean would be rejected if the sample means will be contained within the confidence interval.
9.67 While using the critical value approach to test a hypothesis, the following six steps should be followed.
- The process starts by stating the hypotheses for the test: a null and alternative hypothesis.
- This will be followed by determining a significance level for the test.
- The next step involves the calculation of the test statistic. Suppose the null hypothesis is true, calculate test statistic using sample data.
- Using the test statistic calculated in step three, calculate the p-value.
- Based on the p-value, decide to reject or not to reject the null hypothesis.
- Finally, state a conclusion for the test based on the decision in step five.
9.68 The five-step p-value approach involves:
- Stating the hypotheses for the test.
- Determine a meaningful level of significance.
- Make a decision on whether to use z or t distribution. t is used when the population standard deviation is unknown, while z is used when the population standard deviation is known.
- Collect the sample data and compute the appropriate test statistic as determined in step three.
- Based on the p-value, make a decision whether to reject or not to reject the null hypothesis.