You are working for a government department and your boss, Jane, has asked you t

Question

You are working for a government department and your boss, Jane, has asked you to calculate some results on weekly household income across the state, including a 95% confidence interval for the mean weekly household income that she needs to include in a report. She also says that she is not sure exactly what a 95% confidence interval means and would like you to add an explanation.

You have been supplied with a sample of weekly income figures for 110 households. The data is presented here:

Historically, the standard deviation in weekly household income is $423.

Complete the report to your boss. Give your numeric answers to 2 decimal places.

Dear Jane,

Here are the results gathered from the collected data:

Assuming a population standard deviation in weekly household income of $423, the 95% confidence interval for the mean weekly household income is:

a)

b)This means that

approximately 95% of sample means will be within the interval given above
on approximately 95% of days in a given period the stock makes a return within the interval given above
the population mean weekly household income is definitely within the interval given above
using a process that gives correct results in 95% of cases, the population mean weekly household income is within the interval given above

Weekly household income ($) 1241 2156 1571 803 2216 1448 1335 1726 1726 1296 1773 1607 1152 1568 1483 1695 998 1398 1272 1287 850 2109 2152 1815 1099 1622 2010 2395 1499 2165 1968 1101 2006 1737 1861 1024 1106 1379 1228 1420 1650 1570 1367 1730 1819 1869 1808 1553 1748 1934 1514 1423 1259 1782 1060 1246 1171 940 2786 1614 1656 1358 1833 837 1673 1821 1791 1653 1262 1300 1800 2507 513 2209 1105 1601 1335 1305 1665 915 1465 1995 877 1079 1160 1997 1831 1363 2027 2349 2005 2837 1545 1946 1423 2241 794 1203 2222 1094 1888 1293 1457 1115 645 1592 1721 1741 1369 959

Explanation / Answer

FROM ABOVE average of 110 observations=1559.2

ands std error =std deviation/(n)1/2 =40.33

also for 95% CI, z=1.96

hence confidence interval =sample mean -/+_ z*std error =1480.152 ; 1638.248

using a process that gives correct results in 95% of cases, the population mean weekly household income is within the interval given above

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