Attempt following question by selecting a choice to answer.
B
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?
e BA.
B10,651
B.
B470
C.
B2,237
D.
B223,655
B
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.