Paper Topic:

Elementary Statistics - Sample Size & Confidence Interval

Sample Size and Confidence Interval Problem

Sample Size

How many , if any , additional home prices need to be sampled from your state in to construct a 93 confidence interval , for the population mean , that has a margin of error of at most 10 ,000

terval 93

E 10 ,000 224 ,378 .0993 1 - 0 .93 0 .07 / 2 0 .07 / 2 0 .035

Area 0 .5 - 0 .035 0 .4650

Using table E , the corresponding z value is 1 .81 1 .81

Now to find the sample size of homes , we

will use following formula , can be rounded up to 1 ,650

Therefore , to be 93 confident that the margin of error is at most 10 ,000 , we would need to have 1 ,650 sample prices . Our current sample is 73 prices /homes , thus we would need an addition of 1 ,577 home prices

Confidence Interval

To construct a 90 confidence interval for the proportion (percentage of homes in the state of Virginia that have an advertised selling price of over 300000 , we first need an estimate for the population proportion

a ) Using your sample , state the value of p-hat (See the table you constructed for Problem /Step 6 of the earlier project 38 /73 0 .5205

b ) Using the value you calculated for p-hat for my state of Virginia are n times p-hat and n times q-hat both greater than or equal to 5 Note that n is my sample size ) both are greater than 5

c ) If the answer to part b is yes , then construct the 90 confidence interval for

, the population proportion of homes in Virgina that have an advertised selling price of over 300 ,000 . If your answer to part b is no , then you cannot use the normal distribution to approximate the binomial distribution , but if you would like to try constructing the CI using the normal distribution for the practice then go ahead but note that my instructor informed me the interval is misleading and considered a misuse /abuse of statistics

A confidence interval for the population

is given by Value of Z for 90 1 .645 Confidence interval (CI (0 .4243 , 0 .6167

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h on for the confidence interval you constructed

The above confidence interval (0 .4243 , 0 .6167 ) tells us that we can be 90 confident that the population percentage of homes with a selling price above 300 ,000 in Virgina is between 42 .43 and 61 .67 . In other words , one can be 90 confident that the percentage of all homes for sale in Virgina with a selling price above 300 ,000 is between 42 .43 and 61 .67...

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