Question

How do you determine confidence intervals for differences in means and proportions? Please explain by words...No formula, please.

Answer 1

For construction of confidence interval for the differences in means, we need some values such as sample means of two samples or two groups, sample sizes for two groups, and sample standard deviations for two groups. Also, we need confidence level for finding the confidence interval. There are two cases exists during the construction of confidence interval for the differences in the means. If the population variances are equal, then we use the pooled variance for construction of confidence interval. If population variances are not equal, then we do not use pooled variance. For finding the confidence interval for difference between two population means, we find the sample statistic as the difference between the two sample means. We use t critical value or z critical value depends on the availability of population variances and sample sizes. If sample sizes are too large and population standard deviations are given, then we prefer z confidence interval. If population standard deviations are not given, then we use t critical value for finding confidence interval. Critical values are varies due to different confidence levels and sample sizes.

For the construction of the confidence interval for the difference in population proportions, we only use Z critical value. Like above confidence interval, we do not use other critical value. First we find the difference between two sample proportions. Z critical value can be obtained from z-table or excel or different softwares. We use the pooled proportion for the confidence interval for the difference between population proportions.