Answer:
Distribution will get taller and SD will decrease.
Step-by-step explanation:
Sample Size and Standard Deviation:
In a t-distribution, sample size and standard deviation are inversely related.
A larger sample size results in decreased standard deviation and a smaller sample size will result in increased standard deviation.
Sample Size and Shape of t-distribution:
As we increase the sample size, the corresponding degree of freedom increases which causes the t-distribution to like normal distribution. With a considerably larger sample size, the t-distribution and normal distribution are almost identical.
Degree of freedom = n - 1
Where n is the sample size.
The shape of the t-distribution becomes more taller and less spread out as the sample size is increased
Refer to the attached graphs, where the shape of a t-distribution is shown with respect to degrees of freedom and also t-distribution is compared with normal distribution.
We can clearly notice that as the degree of freedom increases, the shape of the t-distribution becomes taller and narrower which means more data at the center rather than at the tails.
Also notice that as the degree of freedom increases, the shape of the t-distribution approaches normal distribution.
