Ask Question
19 August, 04:29

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

+5
Answers (1)
  1. 19 August, 06:35
    0
    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.
Know the Answer?
Not Sure About the Answer?
Get an answer to your question ✅ “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 ...” in 📙 Mathematics if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions.
Search for Other Answers