In constructing a confidence interval estimate for a population mean, when we replace S with the sample standard deviation (s),
we introduce a new source of variability and the sampling distribution we use is:A. the normal distribution B. F- distribution C. chi-square distribution D. t -distribution
When the population standard deviation is unknown while constructing the confidence interval then the estimate of standard deviation calculated from sample is used and due to this the new type of variability arise and then for conducting a confidence interval for mean the t-distribution is used. For calculating confidence interval for mean there are two sampling distributions z distribution and t distribution. When sample size is small and population standard deviation is unknown then t-distribution is used.
