Question

A tax assessor wants to assess the mean property tax bill for all homeowners in a certain state. From a survey ten years ago, a sample of 14 property tax bills is given below. Assume the property tax bill is approximately normally distributed. Use a TI-83, TI-83 plus, or TI-84 calculator to construct a 90% confidence interval for the population mean property tax bill. Round your answers to one decimal place and use increasing order.
Property Tax Bill
1715.35
1157.82
651.10
1093.36
1609.22
1391.47
1398.89
402.99
1028.76
1571.23
529.42
1579.48
699.56
2222.16
838.60
866.41
1066.60
1498.64
1784.28
2016.99
2465.65
1098.81
1346.65
1574.00
1447.78
2018.33
2156.75
1710.81

Answer 1

Answer:

The answer is below

Step-by-step explanation:

From the table, the mean (μ) = 1390.75 and the standard deviation (σ) = 518.75

The confidence level (C) = 90% = 0.9

α = 1 - C = 1 - 0.9 = 0.1

α/2 = 0.1 / 2 = 0.05

The z score of α/2 (0.05) is the same as the z score of 0.45 (0.5 - 0.05) which is equal to 1.645.

The margin of error (E) is given as:

$E=Z_\frac{\alpha}{2}*\frac{\sigma}{\sqrt{n} } \\\\E=1.645*\frac{518.75}{\sqrt{14} } =228.07$

The confidence interval = μ ± E = 1390.75 ± 228.07 = (1162.68, 1618.82)

The confidence interval is between 1162.68 and 1618.82.