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:

1684
2275
1337
2236
1184
1170
1958
2818
1810
2130
1793
1502
1055
1871
1795
1660
1203
2129
1725
894
1538
982
1912
1451
1248
1152
2240
1926
1630
1821
1517
1762
1415
1337
1722
1637
2142
1120
1851
544
2044
2103
2242
1445
1765
2058
2301
1496
1642
1568
1253
2417
1220
1363
1160
1409
1734
1678
1839
2206
2351
658
1942
1517
1376
2434
1366
2070
1525
1830
2011
1301
1711
1381
1791
998
1027
2097
1928
1254
2054
1373
1884
1336
1353
1714
2305
1735
1433
1739
2151
2148
1494
2030
1668
2082
1515
1377
1499
1720
1720
1963
1831
1292
1515
1533
1252
1805
1257
1411

Historically, the standard deviation in weekly household income is $411.

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 $411, the 95% confidence interval for the mean weekly household income is:

a) _______ ≤ μ ≤ _________

b) This means that option ___ is correct.

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

Answer 1