Attempt following question by selecting a choice to answer.
e
A researcher would like to estimate the proportion of all mothers who take black coffee during pregnancy. She would like to be 90% confident that the estimate is within 2.5 percentage points of the true proportion. What sample size is required?
DDDD eeeeA.
e0.574
B.
e2,178
C.
e0.109
D.
e1,089
ee
D
Step 1: For 90% confident interval, zα/2 is 1.65.[Use the standard normal distribution table.]
Step 2: The maximum error of estimation allowed, E = 2.5% = 0.025
Step 3: For any given sample size, E will be maximized when the sample proportion is 0.5
Step 4: Sample size, n = pˆ qˆ (Zα/2E)2
[Minimum sample size.]
Step 5: n = (0.5) (0.5)(1.650.025)2
n = 1,089[Assuming pˆ = 0.5, qˆ = 1 - pˆ = 0.5.]
Step 6: So, to be 90% confident she requires a sample of 1,089 pregnant women.