STATISTICAL TECHNIQUES AND TOOLS
CONFIDENCE INTERVALS
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Question
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A study found that in a sample of 44 subjects, 9 of agree that children under 6 shouldn’t be taken to nice restaurants. The 95% confidence interval for p is (0.082, 0.318). Interpret this interval.
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95% of the time the proportion of people who believe children under 6 shouldn’t be taken to nice restaurants will be between 8.2% and 31.8%.
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The population proportion of people who believe children under 6 shouldn’t be taken to nice restaurants is between 8.2% and 31.8%.
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The probability that the proportion of people who believe children under 6 shouldn’t be taken to nice restaurants will be between 8.2% and 31.8% is 95%.
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Based on this sample, I am 95% confident that the proportion of people who believe children under 6 shouldn’t be taken to nice restaurants is between 8.2% and 31.8%.
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Explanation:
Detailed explanation-1: -The value of z* for a confidence level of 95% is 1.96.
Detailed explanation-2: -To calculate the confidence interval, we must find p′, q′. p′ = 0.842 is the sample proportion; this is the point estimate of the population proportion. Since the requested confidence level is CL = 0.95, then = 1 – CL = 1 – 0.95 = 0.05 ( 2 ) ( 2 ) = 0.025.
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