8-3 Testing a Claim About a Mean 407 Here are the steps that follow the procedure summarized in Figure 8-1 on page 376. Step 1: The claim that “the mean amount of adult sleep is less than 7 hours” becomes m 6 7 hours when expressed in symbolic form. Step 2: The alternative (in symbolic form) to the original claim is m Ú 7 hours. Step 3: Because the statement m 6 7 hours does not contain the condition of equality, it becomes the alternative hypothesis H1. The null hypothesis H0 is the statement that m = 7 hours. H0: m = 7 hours 1null hypothesis2 H1: m 6 7 hours 1alternative hypothesis and original claim2 Step 4: As specified in the statement of the problem, the significance level is a = 0.05. Step 5: Because the claim is made about the population meanm, the sample statistic most relevant to this test is the sample mean x, and we use the t distribution. Step 6: The sample statistics of n =12, x =6.83333333 hours, s = 1.99240984 hours are used to calculate the test statistic as follows, but technologies provide the test statistic of t = -0.290. In calculations such as the following, it is good to carry extra decimal places and not round. t = x - mx s2 n = 6.83333333 - 7 1.99240984 2 12 = -0.290 P-Value with Technology We could use technology to obtain the P-value. Shown below and on the next page are results from several technologies, and we can see that the P-value is 0.3887 (rounded). (SPSS shows a two-tailed P-value of 0.777, so it must be halved for this one-tailed test.) Step 7: Because the P-value of 0.3887 is greater than the significance level of a = 0.05, we fail to reject the null hypothesis. YOUR TURN. Do Exercise 13 “Systolic Blood Pressure.” INTERPRETATION Step 8: Because we fail to reject the null hypothesis, we conclude that there is not sufficient evidence to support the claim that the mean amount of adult sleep is less than 7 hours. Statdisk Excel (XLSTAT) TI-83, 84 Plus . Go Figure Mastercard alone receives about three Internet attack attempts every second. continued
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