The confidence interval of the T/Z curve represents probability (shaded area under the curve). If the confidence interval expands i.e the gap (standard error x Z/T) increases then the probability of point interval falling in the shaded area increases as confidence interval is bigger, our value range is also bigger [mean +- z(sd)].
For eg. (Two tailed test)
1st Case: If we take Z = 1.96, area under the confidence interval i.e probability is 95% (shaded area).
2nd Case: if Z = 2.33, shaded area i.e confidence interval is 98%. As Z is more in the 2nd case, our value range [mean +- z(sd)] is bigger.
Now, we are 98% confident that our point estimate lies in the value range unlike 95% in the 1st case.
Hello Archana,
The confidence interval of the T/Z curve represents probability (shaded area under the curve). If the confidence interval expands i.e the gap (standard error x Z/T) increases then the probability of point interval falling in the shaded area increases as confidence interval is bigger, our value range is also bigger [mean +- z(sd)].
For eg. (Two tailed test)
1st Case: If we take Z = 1.96, area under the confidence interval i.e probability is 95% (shaded area).
2nd Case: if Z = 2.33, shaded area i.e confidence interval is 98%. As Z is more in the 2nd case, our value range [mean +- z(sd)] is bigger.
Now, we are 98% confident that our point estimate lies in the value range unlike 95% in the 1st case.
Thank u!