RESEARCH METHODOLOGY

Detailed explanation-1: -Up until the mid-1970s, some statisticians used the normal distribution approximation for large sample sizes and used the Student’s t-distribution only for sample sizes of at most 30 observations. However, now when we do not know the population standard deviation, we will use the t-distribution.

Detailed explanation-2: -The t-distribution is most useful for small sample sizes, when the population standard deviation is not known, or both. As the sample size increases, the t-distribution becomes more similar to a normal distribution.

Detailed explanation-3: -To construct a confidence interval for a single unknown population mean , where the population standard deviation is known, we need x-x-as an estimate for and we need the margin of error. Here, the margin of error (EBM) is called the error bound for a population mean (abbreviated EBM).

Detailed explanation-4: -The t distributions is wide (has thicker tailed) for smaller sample sizes, reflecting that s can be smaller than . The thick tails ensure that the 80%, 95% confidence intervals are wider than those of a standard normal distribution (so are better for capturing the population mean).