Respuesta :
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.
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;
[tex]P_1 = \dfrac{140}{244} = 0.6[/tex]
The population proportion of adults under the age of 40 who would use an online dating service is,
[tex]P_2 = \dfrac{131}{234} = 0.56[/tex]
Therefore, The Standard Error is given by,
[tex]Standard\ error = z \times \sqrt{\dfrac{p_1(1-p_1)}{n_1} + \dfrac{p_2 (1-p_2)}{n_2} } \\\\[/tex]
Putting all the values in the given formula,
[tex]= 1.65 \times \sqrt{\dfrac{0.16(1-0.16)}{240} + \dfrac{0.56(1-0.56)}{234} } \\\\\\= 1.65 \times \sqrt{\dfrac{0.16(0.84)}{240} + \dfrac{0.56 (0.44)}{234} } \\\\\\= 1.65 \times \sqrt{0.00056+0.0010}\\\\= 1.65 \times 0.0453\\\\= 0.075[/tex]
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.
To know more about Standard deviation click the link given below.
https://brainly.com/question/11034287
