The options at the end of the question are not typed properly, the correct options are given below.
A. √[144/240(1−144/240)/240] + [131/234(1−131/234)/234]
B. 1.65√[144/240(1−144/240)/240] + [131/234(1−131/234)/234]
C. 1.96√[144/240(1−144/240)/240] + [131/234(1−131/234)/234]
D. √[275/474(1−275/474)/474] + [275/474(1−275/474)/474]
E. 1.65√[275/474(1−275/474)/474] + [275/474(1−275/474)/474]
Given Information:
Confidence interval = 90%
Sample size of adults over the age of 40 = n₁ = 240
Sample size of adults under the age of 40 = n₂ = 234
Number of adults over the age of 40 who would use an online dating service = 144
Number of adults under the age of 40 who would use an online dating service = 131
Required Information:
standard error = ?
Answer:
standard error = 0.075
Step-by-step explanation:
The population proportion of adults over the age of 40 who would use an online dating service is,
p₁ = 144/240
p₁ = 0.6
The population proportion of adults under the age of 40 who would use an online dating service is,
p₂ = 131/234
p₂ = 0.56
The Standard Error is given by
SE = z*√(p₁(1 - p₁)/n₁ + p₂(1 - p₂)/n₂)
Where z is the corresponding z-score value for the 90% confidence level that is 1.65
SE = 1.65*√(0.6(1 - 0.6)/240 + 0.56(1 - 0.56)/234)
This is the equation corresponding to the correct option B given in the question.
SE = 1.65*0.0453
SE = 0.075
Therefore, 0.075 is the standard error for 90% confidence interval to estimate the difference between the population proportions of adults within each age group who would use an online dating service.
