Question

A random sample of 1500 residential telephones in Phoenix found that 390 of the numbers were unlisted. A random sample in the same year of 1200 telephones in Scottsdale found that 304 were unlisted. Round your answers to four decimal places (e.g. 98.7654). (a) Calculate a 95% two-sided confidence interval on the difference in the proportions of unlisted numbers between the two cities. -0.0336 sp1-p2s 0.0329 (b) Is there a significant difference between the two proportions at a = 0.05? No. (c) Calculate a 90% two-sided confidence interval on the difference in the proportions of unlisted numbers between the two cities. sp1-p2s 0.0275 Statistical Tables and Charts -0.0282

Answer 1

MINITAB procedure: Step 1: Choose Stat > Basic Statistics > 2 Proportions. Step 2: Choose Summarized data. Step 3: In First sample, enter Trials as 1500 and Events as 390. Step 4: In Second sample. enter Trials as 1200 and Events as 304. Step 5: Enter Confidence Level as 95%. Check Perform hypothesis test. Step 6: Click OK MINITAB output: Test and CI for Two Proportions Sample 1 2 N Sample p 390 1500 0.260000 304 1200 0.253333 Difference = p (1) - P (2) Estimate for difference: 0.00666667 95% CI for difference: (-0.0264733, 0.0398067) Test for difference - 0 (190): Z-0.39 P-Value - 0.693

The 95% confidence interval is -0.0265 P.-P. 30.0398. (b) No. (c) MINITAB procedure: Step 1: Choose Stat > Basic Statistics > 2 Proportions. Step 2: Choose Summarized data. Step 3: In First sample, enter Trials as 1500 and Events as 390. Step 4: In Second sample. enter Trials as 1200 and Events as 304. Step 5: Enter Confidence Level as 90%. Check Perform hypothesis test. Step 6: Click OK MINITAB output:

Test and CI for Two Proportions Sample 1 2 N Sample p 390 1500 0.260000 304 1200 0.253333 Difference - P(1) - D (2) Estimate for difference: 0.00666667 90% CI for difference: (-0.0211453, 0.0344786) The 90% confidence interval is -0.02113 P.-P. 30.0345.