One year a large number of foreclosed homes in the Washington, DC, metro area we
ID: 3363425 • Letter: O
Question
One year a large number of foreclosed homes in the Washington, DC, metro area were sold. In one community, a sample of 30 foreclosed homes sold for an average of $443,679 with a standard deviation of $19,167. Complete parts (a) through (c) below (a) Suppose the standard deviation of the values was $300,000 instead of the S198,167 used for a confidence interval. What would the larger standard deviation do to the width of the confidence interval (assuming the same level of confidence)? A. A large' standard deviation decreases the standard e" or and will increase the width or the confidenw interval B. A larger standard deviation decreases the standard error and will decrease lhe width of 1he cont dence interval C. A laige' standard devialion rici eases the standard BILr and will decrease lhe width or lhe confidence, interval O D. A larger standard deviation increases the standard error and will increase the width of the confidence interval. b Your dass nale su ests hal he margin c error m he in rval u u d b educe if he confidence merval were changed US0% m e dof 95%. Du ou ag ee with is sialetleri ? why ry y no ? O A. The margin or error is increased when the level ot contidence is reduced This is because a lower level ot contdence captures a smaller percentage o possible sample means B. The rriat m u' error 1s reduced when re eve o con derice is leduced Th s s because a uwer eve o con denue uap utes d al ei per en age of possible sariple rneans C. The margin or emor ts reduced when the level ot con dence is reduced The s because a lower level ot confidence captures a smaller percentage or possible sample means The rnal In ul e ror IS Increased when he eve of u nidency s reduced. This is because a lo er eve of confidence cap res largel percen age o possible sang e means (c) Instead of changing the level of confidence, would it be more statistically appropriate to draw a bigger sample? A. A larger semple size reduces the standard error and thus decrease the margin error B. A larger sample size increases the standard error, and thus decrease the margin of error O C. A laier sample size reduces he slandard eror, and thus increase he margin of ero OD. A larger sample size increases the standard error, and thus increase the margin of errorExplanation / Answer
a. Standard deviation is the numerator of margin of error, increasing its value will increase standard error and finally margin of error with increase which will increase the width of the confidence interval.
Hence answer is D.
b. When we reduce the margin of error, value of t or z reduced, being in numerator smaller value will give smaller margin of error and so width decreases which means it captures smaller percentage of possible sample mean.
Hence answer is C.
c. Now sample size is in denominator, so big the number less the standard error, and if standard error reduces margin of error reduces and width will automatically reduce.
Hence answer is A.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.