Confidence interval z score1/21/2024 Z depends on the level of confidence desired, Where p is the proportion in the sample and p=140/200=0.7, The critical z value for 30% confidence interval is 0.385.Īpplying the general formula for a confidence interval, the confidence interval for a proportion is: , the 95% confidence interval lies between 24.11 and 25.89 Normal Probability Distribution and Confidence Intervals This solution provides a z-distribution calculation for finding the confidence interval, as well as discusses what this interval means. Since Z(0.05/2)< Z(0.01/2) and other values will not change, then the interval will become shorter. Therefore, it is 80% confidence interval.Ĭontinous Probability Distributions - Statistics Therefore, it is 99% confidence interval.ĭ. Therefore, it is 90% confidence interval.Ĭ. The 95% confidence interval is [μ - z * (σ/√n), μ + (b) z- score for 95% confidence is z = 1.96 (a) z- score for 90% confidence is z = 1.645 Therefore the width of the confidence interval increases. When the confidence level increases, the critical value z(alpha/2) increases and hence the margin of error increases. Excel file is included.ī) Construct the 99% confidence interval fro the population proportion.Ĭ) Which interval is wider and why is it wider? Please see the attached file. Therefore, 100 - 2( Z * sigma) percentageĬomputes the the 90% and 95% confidence interval for mean number of hours children watch television per day. Percentage area outside the confidence interval = % Percentage area inside the confidence interval = 2( Z * sigma)% The width of the confidence interval = 2( Z * sigma)
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