Critical Value Approach to Hypothesis Testing
Critical-Value Approach to Hypothesis Testing
We often use inferential statistics to make decisions or judgments about the value of a parameter, such as a population mean. For example, we might need to decide whether the mean weight, μ, of all bags of pretzels packaged by a particular company differs from the advertised weight of 454 grams (g), or we might want to determine whether the mean age, μ, of all cars in use has increased from the year 2000 mean of 9.0 years. One of the most commonly used methods for making such decisions or judgments are to perform a hypothesis test.
With the critical-value approach to hypothesis testing, we choose a “cutoff point” (or cutoff points) based on the significance level of the hypothesis test. The criterion for deciding whether to reject the null hypothesis involves a comparison of the value of the test statistic to the cutoff point(s). The set of values for the test statistic that leads us to reject the null hypothesis is called the rejection region. The set of values for the test statistic that leads us not to reject the null hypothesis is called the non-rejection region. The value of the test statistic that separates the rejection and non-rejection region (i.e., the cutoff point) is called the critical value.
Suppose that a hypothesis test is to be performed at the significance level α. Then the critical value(s) must be chosen so that, if the null hypothesis is true, the probability is α that the test statistic will fall in the rejection region. If the value of the test statistic falls in the rejection region, reject the null hypothesis; otherwise, do not reject the null hypothesis.
• Rejection region: The set of values for the test statistic that leads to rejection of the null hypothesis.
• Non-rejection region: The set of values for the test statistic that leads to non-rejection of the null hypothesis.
Any decision we make based on a hypothesis test may be incorrect because we have used partial
We often use inferential statistics to make decisions or judgments about the value of a parameter, such as a population mean. For example, we might need to decide whether the mean weight, μ, of all bags of pretzels packaged by a particular company differs from the advertised weight of 454 grams (g), or we might want to determine whether the mean age, μ, of all cars in use has increased from the year 2000 mean of 9.0 years. One of the most commonly used methods for making such decisions or judgments are to perform a hypothesis test.
With the critical-value approach to hypothesis testing, we choose a “cutoff point” (or cutoff points) based on the significance level of the hypothesis test. The criterion for deciding whether to reject the null hypothesis involves a comparison of the value of the test statistic to the cutoff point(s). The set of values for the test statistic that leads us to reject the null hypothesis is called the rejection region. The set of values for the test statistic that leads us not to reject the null hypothesis is called the non-rejection region. The value of the test statistic that separates the rejection and non-rejection region (i.e., the cutoff point) is called the critical value.
Suppose that a hypothesis test is to be performed at the significance level α. Then the critical value(s) must be chosen so that, if the null hypothesis is true, the probability is α that the test statistic will fall in the rejection region. If the value of the test statistic falls in the rejection region, reject the null hypothesis; otherwise, do not reject the null hypothesis.
• Rejection region: The set of values for the test statistic that leads to rejection of the null hypothesis.
• Non-rejection region: The set of values for the test statistic that leads to non-rejection of the null hypothesis.
Any decision we make based on a hypothesis test may be incorrect because we have used partial