Section 7-4 Hypothesis Test for Proportions Make sure that np and nq are both ≥ 5. Test statistic is 𝑝 (the sample proportion), and the standardized test statistic is z. Stat Test 5 (1-PropZTest) The first value you enter is the proportion given in the claim. The second and third values you enter come from the sample results. Designate the type of test (left, right, or two-tailed) Once you have p, the decision making process is the same as we’ve been doing all chapter.

z-test for a proportion p (Large Sample) SECTION 7-4 z-test for a proportion p (Large Sample) (np & nq both > 5) Identify H0 and Ha Identify α STAT Test Find p If p α, Reject H0 If p α, Fail to reject H0 Find t Find the critical value(s) and rejection region(s) Use invNorm (2nd VARS 3) functions: Left-tailed test, use Right-tailed test, use Two-tailed test, use If standardized test statistic (z) is rejection region, reject H0. If standardized test statistic (z) is rejection region, fail to reject H0 5 ≤ > α 1 – α α / 2 in the NOT in the

Section 7-4 Example 1 (Page 408) A research center claims that less than 20% of Internet users in the United States have a wireless network in their home. In a random sample of 100 adults, 15% say they have a wireless network in their home. At 𝛼=0.01, is there enough evidence to support the researchers’ claim? First, check to be sure that np and nq are both ≥ 5. 100(.2) = 20, and 100(.8) = 80, so we are good on that. Second, write your hypotheses and identify the claim. 𝐻 0: 𝑝≥0.20 𝐻 𝑎: 𝑝<0.20 (claim) This is a left-tailed test, determined by the 𝐻 𝑎 .

Section 7-4 STAT Test 5 Enter .2 (the p in the claim), 15 (15% of 100 is 15), 100 (n =100), and select < for left-tailed test. p = .1056 z = -1.25 Compare p to 𝛼. Since .1056 > 0.01, fail to reject 𝐻 0 . This means that you can NOT support the claim.

Section 7-4 Example 2 (Page 409) Zogby International claims that 45% of people in the United States support making cigarettes illegal within the next 5 to 10 years. You decide to test this claim and ask a random sample of 200 people in the United States whether they support making cigarettes illegal within the next 5 to 10 years. Of the 200 people, 49% support this law. At 𝛼=0.05, is there enough evidence to reject this claim? First, check to be sure that np and nq are both ≥ 5. 200(.45) = 90, and 200(.55) = 110; we are good on that. Second, write your hypotheses and identify the claim. 𝐻 0: 𝑝=0.45 (claim) 𝐻 𝑎: 𝑝≠0.45 This is a two-tailed test, determined by the 𝐻 𝑎 .

Section 7-4 STAT Test 5 Enter .45 (the p in the claim), 98 (49% of 200 is 98), 200 (n = 200), and select ≠ for two-tailed test. p = .2555 z = 1.137 Compare p to 𝛼. Since .2555 > 0.05, fail to reject 𝐻 0 . This means that you can NOT reject the claim.

Section 7-4 Example 3 (Page 410) The Pew Research Center claims that more than 55% of U.S. adults regularly watch their local television news. You decide to test this claim and ask a random sample of 425 adults in the United States whether they regularly watch their local television news. Of the 425 adults, 255 respond yes. At 𝛼=0.05, is there enough evidence to support the claim? First, check to be sure that np and nq are both ≥ 5. 425(.55) = 233.75, and 425(.45) = 191.25; we are good. Second, write your hypotheses and identify the claim. 𝐻 0: 𝑝≤0.55 𝐻 𝑎: 𝑝>0.55 (claim) This is a right-tailed test, determined by the 𝐻 𝑎 .

Section 7-4 STAT Test 5 Enter .55 (the p in the claim), 255 (x = 255), 425 (n = 425), and select > for right-tailed test. p = .0191 z = 2.0719 Compare p to 𝛼. Since .0191 ≤ 0.05, reject 𝐻 0 . This means that you CAN support the claim.

Assignments: Classwork: Page 411 #3-8 All Homework: Pages 411-412 # 9-16 All FOR THE HOMEWORK, SIMPLY DO THE P-TEST. Ignore part b); no need to find the critical values or the rejection regions.