confidence interval for proportion


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PDF 45 Confidence Intervals for a Proportion

Calculate a 95 confidence interval (CI) of proportion p of purchase slips made with Visa (a) Point estimate Point estimate of population (actual true) 

  • How do you find the confidence interval for a proportion?

    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 α = 1 – CL = 1 – 0.95 = 0.05 ( α 2 ) ( α 2 ) = 0.025.13 déc. 2023

  • p̂ is the sample proportion (x/n), Z is the Z-value corresponding to the desired confidence level (90% confidence level corresponds to a Z-value of approximately 1.645), n is the sample size.
    Thus, the 90% confidence interval for the population proportion is approximately 0.5431 to 0.6569.

  • What is meant by the 99% confidence interval for a proportion?

    Confidence interval of the proportion
    Therefore, the 99% confidence interval is 0.37 to 0.43.
    That is, we are 99% confident that the true proportion is in the range 0.37 to 0.43.

  • How to construct a 95% confidence interval for the true proportion?

    1For the interval of the sample mean:2A 95 % confidence interval goes from 2.5% to 97.5 %3If you look up P(z< Z) = 0.975 (the upper limit)4Z_critical = 1.96 (From any z-table)5Standard error = +/- Z_critical* population standard deviation/sqrt(N)6Population standard deviation = sqrt(2.3)

  • Similar to confidence intervals for population means, a confidence interval for a population proportion is constructed by taking a sample of size n from the population, calculating the sample proportion ^p , and then adding and subtracting the margin of error from ^p to get the limits of the confidence interval.
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