Question

Can someone explain why these answers are false? I posted my thinking behind what I think the answer is. Please let me know if my approach is correct.

1.) In general, the larger the value of the standard error, the more NARROW or WIDER becomes the confidence Interval.

My Rationale After Rereading The Question: Standard Error is like Standard deviation right? If you have a large deviation, your not completely sure where your mean value is. Therefore it is better to have a wider interval just in case your mean value lies within the wide interval. However, if you have a small standard error (say 0.0005) your confident that your mean value is true and the interval becomes narrower or more specific.

2.) In general, as sample size increases, the width of the confidence interval also increaes (True or False)

I can't understand this question. Is the answer false because as you increase the sample size, you approach a normal distribution. And when you have a normal distribution it is easy to tell what the mean value is , so you can narrow down your confidence interval to a specific range?

Answer 1

1)

Answer:- the standard error is calculated by dividing standard deviation by square root of sample size.

Standard deviation is large means values in the sample deviate more from the mean value. So we calculate standard error i.e. we can make an error when develope confidence interval.so we calculate margin of error i.e. how much values of the mean can deviate from the mean.

So if we get standard error large then the margin of error would be large and so confidence interval. and vice versa.

So if standard error is large confidence interval would be wider & for small standard error confidence interval would be smaller.

2. If we increase the sample size the confidence interval decreases.

the standard error depends on sample size and standard deviation

As sample size increases standard error decreases. because we divide standard deviation by square root of sample size.

as decrease standard error then confidence interval would be decreased.