## Saturday, August 24, 2019

### Proportion Paper Essay Example | Topics and Well Written Essays - 750 words

Proportion Paper - Essay Example for a proportion, sample size required for a proportion, confidence interval for the difference of two proportion, comparison of a proportion with hypothesized proportion, and comparison of two proportions will be discussed. Central Limit Theorem (CLT) for a Proportion state that Ã¢â‚¬Å"As sample size increases, the distribution of the sample proportion p = x/n approaches a normal distribution with mean Ãâ‚¬ and standard deviation.Ã¢â‚¬  The statistic p = x/n is assumed normally distributed when the sample is large. A conservative rule of thumb that normality may be assumed whenever nÃâ‚¬ Ã¢â€° ¥ 10 and n(1 Ã¢Ë†â€™ Ãâ‚¬) Ã¢â€° ¥ 10. This rule requires a very large sample size to assume normality when Ãâ‚¬ differs greatly from 0.50 (Doane & Seward 2007). Using the Central Limit Theorem, the probability that a sample proportion will fall within a given interval can be stated. The confidence interval for a population proportion, Ãâ‚¬ at a given confidence level (1 Ã¢â‚¬â€œ ÃŽ ±) is given by The value of z can be obtained using normal table (Z table) or using Excel function NORMINV(ÃŽ ±/2). The width of the confidence interval for a population proportion, Ãâ‚¬ depends on the sample size, confidence level (1 Ã¢â‚¬â€œ ÃŽ ±), and the sample proportion p. The estimate of difference and standard deviation of two-population proportion can be given by and , respectively. Using this estimate, a confidence interval for the difference of two population proportions, (Ãâ‚¬1Ã¢Ë†â€™ Ãâ‚¬2), is given by For normal sampling distribution, the test statistic for the hypothesis test will be z score. This test statistic is compared with critical value of z score at the selected level of significance, ÃŽ ± for retaining or rejecting null hypothesis (H0). The test statistic for a population proportion with hypothesized proportion Ãâ‚¬0 is the difference between the sample proportion p and the hypothesized proportion Ãâ‚¬0 divided by the estimated standard error of the proportion (denoted ÃÆ'p) as given below The assumptions of comparison