10.3 Confidence Intervals for Proportions (z distribution)
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Lab 10.3.1
In a random sample of 120 adults, 51 are fully vaccinated for Covid19. Construct a 90% confidence interval using the conf_prop function above.
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The two z* values these three labs need
conf_prop needs the same normal critical value as conf_z_mean, and the three labs in this section use two different confidence levels. 90% is the first link: 1.6448536269514722. 95%, which Lab 10.3.2 asks for, is the second: 1.959963984540054. The sample proportion, the margin of error and the sample-size formula in Lab 10.3.3 are yours to assemble.
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Lab 10.3.1, already computed
The 1-Proportion Z Interval panel opens on the lab's own counts - 51 successes out of 120 trials at confidence 0.90 - and returns Sample Proportion 0.425000 with the interval 0.350772 to 0.499228. Notice what that interval does NOT contain: 0.5. The book's answer key computes p = 51/120 and prints ( 0.3507724679563704, 0.4992275320436296 ), the same two numbers. Assemble it yourself with conf_prop first; open this afterwards.
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Lab 10.3.2
In a random sample of 120 adults, 50% are fully vaccinated for Covid19. Construct a 95% confidence interval using the conf_prop function above.
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Lab 10.3.2, already computed - and why the panel wants a count
The panel takes successes and trials rather than a percentage, so the lab's 50% of 120 adults goes in as x = 60, n = 120; it reports Sample Proportion 0.500000, exactly the p the lab states. At confidence 0.95 the interval is 0.410540 to 0.589460 - the book's answer key runs conf_prop(.95,.5,120) and prints ( 0.41054029281414217, 0.5894597071858578 ). Compare it with Lab 10.3.1's interval above: same sample size, wider interval, because 95% confidence costs more width than 90% AND p-hat = 0.5 is where p(1-p) is largest.
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Lab 10.3.3
Town officials want to determine the current percentage of residents vaccinated for Covid19. How many residents should be surveyed in order to be 90% confident that the estimated proportion is within five percentage points of the true population proportion who are vaccinated for Covid19? Previously the proportion was 0.55. Use the samp_pro function below.
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Adapted from Python for Introductory Statistics: Student's Lab Workbook, by Simon Aman (Truman College, City Colleges of Chicago), licensed under CC BY 4.0. Changes were made: reformatted as an accessible XYZ web edition with live in-browser code cells. License: CC-BY-4.0 .
