448 CHAPTER 9 Inferences from Two Samples interval estimate of the difference between two proportions, we don’t assume that the two proportions are equal, and we estimate the standard deviation as Bpn 1q n 1 n1 + pn 2q n 2 n2 In the test statistic z = 1pn 1 - p n 22 - 1p1 - p22 Bpn 1q n 1 n1 + pn 2q n 2 n2 use the positive and negative values of z (for two tails) and solve for p1 - p2. The results are the limits of the confidence interval given in the Key Elements box near the beginning of this section. Inferences with Two Proportions Access tech supplements, videos, and data sets at www.TriolaStats.com TECH CENTER Statdisk Hypothesis Testing 1. Click Analysis in the top menu. 2. Select Hypothesis Testing from the dropdown menu and Proportion Two Samples from the submenu. 3. Select the desired format for Alternative Hypothesis and enter the significance level. For both samples, enter sample size and number of successes. 4. Click Evaluate. Confidence Intervals 1. Click Analysis in the top menu. 2. Select Confidence Intervals from the dropdown menu and Proportion Two Samples from the submenu. 3. Enter the desired confidence level. For both samples, enter sample size and number of successes. 4. Click Evaluate. StatCrunch 1. Click Stat in the top menu. 2. Select Proportion Stats from the dropdown menu, then select Two Sample—With Summary from the submenu. 3. Enter the number of successes and number of observations for both samples. 4. Hypothesis Testing: Select Hypothesis test for p1@p2. Enter 0 for the hypothesized difference 1H02 and select the desired format for the alternative hypothesis 1HA2. Confidence Intervals: Select Confidence interval for p1@p2 and enter the confidence level. 5. Click Compute! Minitab 1. Click Stat in the top menu. 2. Select Basic Statistics from the dropdown menu and select 2 Proportions from the submenu. 3. Select Summarized data from the dropdown menu and enter the number of events and number of trials for both samples. 4. Click the Options button and enter the confidence level. If testing a hypothesis, enter 0 for Hypothesized difference and select the desired format for the Alternative hypothesis. 5. For Test method select Use the pooled estimate of the proportion. 6. Click OK twice. TIP: Another procedure is to click on Assistant in the top menu, then select Hypothesis Tests and 2-Sample % Defective. Complete the dialog box to get results, including P-value and other helpful information. TI-83, 83 84 Plus Calculator 8 us Ca cu ato Hypothesis Testing: 1. Press K, then select TESTS in the top menu. 2. Select 2-PropZTest in the menu and press [. 3. Enter the number of successes (x) and number of observations (n) for both samples. Select the desired format for the alternative hypothesis (p1). 4. Select Calculate and press [. Confidence Intervals: 1. Press K, then select TESTS in the top menu. 2. Select 2-PropZInt in the menu and press [. 3. Enter the number of successes (x) and number of observations (n) for both samples. Enter the desired confidence level (C-Level). 4. Select Calculate and press [. in tw Go Figure Scam calls: It has been estimated that in a recent year, 44.6% of total mobile calls were scam calls (based on a First Orion study of 50 billion mobile calls).
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