Question

1.For a given confidence level 100(1 – α)% (e.g., when α=0.05 the confidence level is 95%) and population standard deviation σ, the width of the confidence interval for the population mean is wider, the smaller the sample size n. (True or False)2.The tdf distribution consists of a family of distributions where the actual shape of each one depends on the degrees of freedom, df. For lower values of df, the tdf distribution is similar to the z distribution. (True or False)

Answer 1

Answer:

1) True

2) False

Step-by-step explanation:

1.

Since the standard error varies directly with the width of the confidence intervals, and the standard error is inversely proportional to the sample size based on the formula :$SE = \frac{\sigma}{\sqrt{n} }$

Where n = sample size and

SE = standard Error

then the width of the confidence increases with smaller sample size.

Answer =True

2)The reverse of this statement is the case

As the degree of freedom  increases, the distribution of the tdf becomes similar to the z distribution and not the other way round

Answer = False