378 CHAPTER 8 Hypothesis Testing ■ Identify H0: The null hypothesis H0 is the symbolic expression that the parameter equals the fixed value being considered, so we get H0: p = 0.5 The first three steps yield the null and alternative hypotheses: H0: p = 0.5 1null hypothesis2 H1: p 7 0.5 1alternative hypothesis2 Note About Forming Your Own Claims (Hypotheses) If you are conducting a study and want to use a hypothesis test to support your claim, your claim must be worded so that it becomes the alternative hypothesis (and can be expressed using only the symbols 6, 7, or ≠). You can never support a claim that a parameter is equal to a specified value. Step 4: Select the Significance Level A DEFINITION The significance level a for a hypothesis test is the probability value used as the cutoff for determining when the sample evidence constitutes significant evidence against the null hypothesis. By its nature, the significance level a is the probability of mistakenly rejecting the null hypothesis when it is true: Significance level A = P1rejecting H0 when H0 is true2 The significance level a is the same a introduced in Section 7-1, where we defined “critical value.” Common choices for a are 0.05, 0.01, and 0.10; 0.05 is most common. Step 5: Identify the Statistic Relevant to the Test and Determine Its Sampling Distribution (such as normal, t, or X2) Table 8-2 lists parameters along with the corresponding sampling distributions. Example: The claim p 7 0.5 is a claim about the population proportion p, so use the normal distribution, provided that the requirements are satisfied. (With n = 926, p = 0.5, and q = 0.5 from Example 1, np Ú 5 and nq Ú 5 are both true.) TABLE 8-2 Parameters and Corresponding Test Statistics Parameter Sampling Distribution Requirements Test Statistic Proportion p Normal (z) np Ú 5 andnq Ú 5 z = pn - p Apq n Mean m t s not known and normally distributed population or s not known and n 7 30 t = x - m s2 n Mean m Normal (z) s known and normally distributed population or s known and n 7 30 z = x - m s2 n St. dev. s or variance s2 x2 Strict requirement: normally distributed population x2 = 1n - 12s2 s 2 T “c S Go Figure 140,000,000,000,000,000,000 miles: The distance you can see with your naked eye. What you see is light from 2.4 million years ago.
RkJQdWJsaXNoZXIy NjM5ODQ=