A random sample of 240 adults over the age of 40 found that 144 would use an online dating service. Another random sample of 234 adults age 40 and under showed that 131 would use an online dating service. Assuming all conditions are met, which of the following is the standard error for a 90 percent confidence interval to estimate the difference between the population proportions of adults within each age group who would use an online dating service?A) 1.44240 B) 1.65144240 C) 1.96144240 D) 2.75474 E) 1.65275474

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.

Given that,

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

We have to determine,

The standard error  for a 90 percent confidence interval to estimate the difference between the population proportions of adults within each age group who would use an online dating service.

According to the question,

The population proportion of adults over the age of 40 who would use an online dating service is;

 The population proportion of adults under the age of 40 who would use an online dating service is,

Therefore, The Standard Error is given by,

Putting all the values in the given formula,

Hence,  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.

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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 = ?

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.