True or false? A larger sample size produces a longer confidence interval for u . Statistics homework.?

Question

True or false? A larger sample size produces a longer confidence interval for u . Statistics homework.?

Answer 1

Larger Sample Size Confidence Interval

Answer 2

Hi,



False. As the sample size increases, the maximal error decreases, resulting in a shorter confidence interval.



It's simple because if you have larger sample, you can predict correctly about various statistical references thus the size of confidence interval will get shorten.



Hope this helps.



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Answer 3

Ok, so when you use a larger sample size, you are polling more people and therefore have a better chance of getting accurate results. For example, if you were trying to figure out average height in a class of 20 and you only asked 3 people, that wouldn't necessarily be an accurate representation of the class as a whole (you could have got the 3 shortest people or the 3 tallest people)… as you ask more and more people in the class, the results will get closer and closer to the actual average-- that is, you will have less error the more people you poll.

Therefore, a larger sample size will decrease maximal error, so we can eliminate options B and C



This leaves us with A and D, and the question is now: "will the confidence interval be shorter or longer"

if you only sampled 3 people, you are not very sure that the average height you found is accurate. For example, if you find the average height is 5'8", then the actual average could be a wide variety of answers because you have no idea if you polled the shortest or tallest people in the class…… so the average height could be a range of numbers anywhere from 4 foot-7foot (which would be a very long confidence interval because it goes all the way from 4-7 on the number line)



BUT, if you polled all 20 people in the class you would know the EXACT average for the class that is 100% correct, so, say you know for sure the average is 5'7" then that is a very short confidence interval because it is an exact point on the number line



therefore the confidence interval will get shorter and shorter as you add more people, so the answer is A