The manager (collections) of the bank feels that the proportion of the number of such credit card holders in the city – X is not different from the proportion of the number of such credit card holders in the city – Y. to test his intuition, a sample of 200 credit card holders is taken from the city – X and it is found that 160 of them are settling their excess withdrawal amount in – time without attracting interest. City Y = 180 credit card holders, 50 customers excess withdrawal in time, City X 80% customers settles their excess withdrawal in time (160/200 = 0.8) Similarly, a sample of 180 credit card holders is taken from the city – Y and it is found that 50 of them are settling their excess withdrawal amount in – time without attracting interest, check the intuition of the sales manager at a significance level of 0.05. 3. A 95% or 0.95 confidence interval corresponds to alpha = 1 – 0.95 = 0.05. As the sample size is the same, the denominator should have been 100 instead of 200 to have the correct sample SD. In fact, there are other approaches that generally yield more accurate results, especially for smaller samples. This is how we can use sample proportion to create a confidence interval, an estimate for what the population proportion might have been. One approach is to estimate the power using the chi-square test. Would you review the standard deviation calculation for Example 4? The number of credit card holders of a bank in two different cities (city – X and city – Y) settling their excess withdrawal amounts in time without attracting interest follows binomial distribution. Thanks for bringing this to my attention and sorry that I didn’t see it earlier. This described at I will take a look at these references. On the Edit menu, click Paste. I’m not sure why this formula is incorrect and doesn’t return the same value as your calculation since they should both be equivalent and I’m not sure how I set up the CONFIDENCE equation incorrectly. Charles. Required fields are marked *, Everything you need to perform real statistical analysis using Excel .. … … .. © Real Statistics 2020. =CONFIDENCE(alpha,standard_dev,size) The CONFIDENCE function uses the following arguments: 1. You want to compute a 95% confidence interval for the population mean. Standard_dev (required argument) – This is the standard deviation for the data range. Apologies too to Sun Kim since I overlooked her comment. variance? mean and variance equal to the pop. I think it would be difficult for me to respect the condition of [ ni πi ≥ 5 and ni (1 –πi) ≥ 5 ] since the πi is pretty close to 0 (in the order of 0.00008) . One approach is to use the approach described for Example 4 on this webpage. 2. To find the confidence interval at 95% I used the Excel equation =CONFIDENCE(0.025, 0.01505, 1100) and got the value 0.00102. I have now corrected the error on the webpage. The result is more involved algebra (which involves solving a quadratic equation), and a more complicated solution. Charles. To find the confidence interval at 95% I used the Excel equation =CONFIDENCE(0.025, 0.01505, 1100) and got the value 0.00102. http://www.biostathandbook.com/fishers.html Thanks for catching this error. City X 30% customers settles their excess withdrawal in time (50/180 = 0.3) Hakan just brought up the same issue. If x is a random variable with binomial distribution B(n, p) then the random variable y = x/n is said to have a proportion distribution. You are correct that the denominator should be 100. So, a significance level of 0.05 is equal to a 95% confidence level. Confidence Interval for Population Proportion in Excel. ... statistical studies, sampling, and confidence intervals. Using the binomial distribution model to determine whether the bank manager institution is true is shown below. But as Sun Kim pointed out above, in this example, I think the denominator for the standard deviation estimate should be 100, not 200, because the estimate of the common variance (when pi_1 = pi_2 = pi) is: pi*(1 – pi)*(1/n_1 + 1/n_2) (and not pi*(1 – pi)/(n_1 + n_2)), Hi Hakan, Khibox, I see two problems with the formula =CONFIDENCE(0.025, 0.01505, 1100) Charles. Jonathan, Apologies for overlooking your comment from a long time ago. This approach is described at You are correct. I have belatedly corrected this error. we estimate its value from the sample, namely, 160 + 50 = 210 successes out of 380, i.e. By serching a little bit, I found that we could use Fisher’s exact test, but i dont know how to conduct a power analysis for this test. The common proportion pi is calculated with denominator 200 = n_1 + n_2. Thanks. I have a question concerning the two sample hypothesis test. q. Your email address will not be published. Charles. Charles, This a two sample hypothesis test. Multinomial and Ordinal Logistic Regression, Linear Algebra and Advanced Matrix Topics, http://www.biostathandbook.com/fishers.html, https://stats.stackexchange.com/questions/133441/computing-the-power-of-fishers-exact-test-in-r, https://stats.stackexchange.com/questions/35940/simulation-of-logistic-regression-power-analysis-designed-experiments/35994#35994, Hypothesis Testing for Binomial Distribution, Relationship between Binomial and Normal Distributions, Negative Binomial and Geometric Distributions, Statistical Power for the Binomial Distribution, Required Sample Size for the Binomial Testing. This formula creates an interval with a lower bound and an upper bound, which likely contains a population parameter with a certain level of confidence: Confidence Interval = [lower bound, upper bound] This tutorial explains how to calculate the following confidence intervals in Excel: 1. https://stats.stackexchange.com/questions/133441/computing-the-power-of-fishers-exact-test-in-r I show how to estimate the effect size using this approach on the website. What test should you use? I want to conduct a power analysis in order to determine the sample size to compare two differents proportions. Charles. ˆ ˆ ˆ / (4) = ± α / 2 p p z pq n. The Wilson Score method does not make the approximation in equation 3. I’m not sure why this formula is incorrect and doesn’t return the same value as your calculation since they should both be equivalent and I’m not sure how I set up the CONFIDENCE equation incorrectly. Could you recommend a book or a reference that explain the calculation of the power analysis for different test.
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