402 CHAPTER 7 Hypothesis Testing with One Sample 7 A Summary of Hypothesis Testing With hypothesis testing, perhaps more than any other area of statistics, it can be difficult to see the overall picture. So, a summary of what you studied in this chapter is provided below. Writing the Hypotheses You are given a claim about a population parameter m, p, s 2, or s. Rewrite the claim and its complement using …, Ú, = and 7, 6, ≠. H0 Ha Identify the claim. Is it H0 or Ha? Specifying a Level of Significance Specify a, the maximum acceptable probability of rejecting a valid H0 (a type I error). Specifying the Sample Size Specify your sample size n. Choosing the Test V Normally distributed population O Any population Mean: H0 describes a hypothesized population mean m. V Use a z@test when s is known and the population is normal. O Use a z@test for any population when s is known and n Ú 30. V Use a t@test when s is not known and the population is normal. O Use a t@test for any population when s is not known and n Ú 30. Proportion: H0 describes a hypothesized population proportion p. O Use a z@test for any population when np Ú 5 and nq Ú 5. Variance or Standard Deviation: H0 describes a hypothesized population variance s 2 or standard deviation s. V Use a chi-square test when the population is normal. Sketching the Sampling Distribution Use Ha to decide whether the test is left-tailed, right-tailed, or two-tailed. Finding the Standardized Test Statistic Take a random sample of size n from the population. Determine the test statistic x, np, or s2. Compute the standardized test statistic z, t, or x 2. Making a Decision Option 1. Decision based on rejection region Use a to find the critical value(s) z0, t0, or x 2 0 and rejection region(s). Decision Rule: Reject H0 when the standardized test statistic is in the rejection region. Fail to reject H0 when the standardized test statistic is not in the rejection region. Option 2. Decision based on P@value Use the standardized test statistic or technology to find the P@value. Decision Rule: Reject H0 when P … a. Fail to reject H0 when P 7 a. Study Tip Large sample sizes will usually increase the cost and effort of testing a hypothesis, but they also tend to make your decision more reliable.
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