Attempt following question by selecting a choice to answer.
D
An economist wishes to estimate the average monthly rent of houses in a large city to within $25 with 99% confidence. A study of 70 houses in the city found that 49 houses had their rent as $1,000. How many houses must be surveyed in order to be justified in assuming that the sample proportion is approximately normally distributed?
cccc DDDDA.
D10,651
B.
D470
C.
D2,237
D.
D223,655
DD
C
Step 1: For 99% confidence interval, zα/2 is 2.58.[Use the standard normal distribution table.]
Step 2: The maximum error of estimation allowed, E = 0.025[$25 of $1000 is 2.5% = 0.025.]
Step 3: pˆ = xn = 4970 = 0.7,
qˆ = 1 - pˆ = 1 - 0.7 = 0.3
Step 4: Sample size, n = pˆ qˆ (Zα/2E)2[Minimum sample size.]
Step 5: n = (0.7) (0.3) (2.580.025)2 = 2,236.55 ≈ 2,237
Step 6: So, to be 99% confident, the economist should survey atleast 2,237 houses.