Respuesta :
Answer:
[tex]s= \sqrt{\frac{0.2(1-0.2)}{125} +\frac{0.9 (1-0.9)}{175}} =0.0424[/tex]
And the best option would be:
A) 0.0424
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
[tex]p_A[/tex] represent the real population proportion for the first case A
[tex] p_A =0.2[/tex] represent the proportion for case A
[tex]n_A=125[/tex] is the sample size selected for A
[tex]p_B[/tex] represent the real population proportion for case B
[tex]\hat p_B =0.9[/tex] represent the estimated proportion for case B
[tex]n_B=175[/tex] is the sample size required for case B
[tex]z[/tex] represent the critical value for the margin of error
Solution to the problem
The population individual proportion have the following distribution
[tex]p \sim N(p,\sqrt{\frac{p(1-p)}{n}})[/tex]
And the standard deviation for the difference of proportions woud be given by:
[tex] s= \sqrt{\frac{\hat p_A(1-\hat p_A)}{n_A} +\frac{\hat p_B (1-\hat p_B)}{n_B}}[/tex]
And replacing we got:
[tex]s= \sqrt{\frac{0.2(1-0.2)}{125} +\frac{0.9 (1-0.9)}{175}} =0.0424[/tex]
And the best option would be:
A) 0.0424
The standard deviation of the sampling distribution for the difference in sample proportions is option A. 0.0424
Given information:
A simple random sample (SRS) of 125 is taken from a population with a 0.2 proportion of success. An independent SRS of 175 is taken from a population with a 0.9 proportion of success.
Calculation of the standard deviation:
[tex]= \sqrt{\frac{0.2(1-0.2)}{125} + \frac{0.9(1-0.9)}{175} }[/tex]
= 0.0424
Learn more about the sample here: https://brainly.com/question/19585705
