CHILD DEVELOPMENT PEDAGOGY

Detailed explanation-1: -What happens to the shape of Student’s t distribution as the degrees of freedom increase? As the degrees of freedom increase, Student’s t distribution becomes less leptokurtic, meaning that the probability of extreme values decreases. The distribution becomes more and more similar to a standard normal distribution.

Detailed explanation-2: -As the DF decreases, the t-distribution has thicker tails. This property allows for the greater uncertainty associated with small sample sizes.

Detailed explanation-3: -TheTh t-distribution has less spread as the degrees of freedom increase because, as n increases, s becomes closer to sigma by the law of large numbers. As the sample size n increases, the density curve of t gets closer to the standard normal density curve.

Detailed explanation-4: -As the df increases, the distribution becomes narrower and less leptokurtic. It becomes increasing similar to a standard normal distribution. When df ≥ 30, Student’s t distribution is almost the same as a standard normal distribution.

Detailed explanation-5: -What is the relationship between the value for degrees of freedom and the shape of the t distribution? As the degrees of freedom increases, the t distribution becomes less spread out.