Respuesta :
Answer: 0.0125
Step-by-step explanation:
Given : A survey by the Pew Research Center asked a random sample of 2142 U.S. adults and a random sample of 1055 college presidents how they would "rate the job the higher education system is doing in providing value for the money.
5% the U.S. adults and 17% of the college presidents provided a rating of "Excellent."
i.e. [tex]n_1=2142,\ n_2=1055[/tex]
[tex]p_1=0.05[/tex] , [tex]p_2=0.17[/tex]
The standard error of the difference in sample proportions :-
[tex]\sqrt{\dfrac{p_1(1-p_1)}{n_1}+\dfrac{p_2(1-p_2)}{n_2}}[/tex]
[tex]=\sqrt{\dfrac{0.05(1-0.05)}{2142}+\dfrac{0.17(1-0.17)}{1055}}\\\\=0.0124867775151\approx0.0125[/tex]
Hence, the standard error of the difference in sample proportion = 0.0125
Finding each variance and then applying the standard error, it is found that the standard error of the difference in sample proportions is of 0.0125.
For a proportion p in a sample of size n, the variances is given by:
[tex]v = \frac{p(1-p)}{n}[/tex]
The standard error of the difference of two sample proportions is the square root of the sum of the variances.
Sample of adults:
- Proportion of 5%, thus [tex]p = 0.05[/tex]
- Sample of 2142, thus [tex]n = 2142[/tex]
The variance is:
[tex]v_A = \frac{0.05(0.95)}{2142}[/tex]
Sample of presidents:
- Proportion of 17%, thus [tex]p = 0.17[/tex]
- Sample of 1055 , thus [tex]n = 1055[/tex]
The variance is:
[tex]v_P = \frac{0.17(0.83)}{1055}[/tex]
Then, the standard error is:
[tex]s = \sqrt{v_A + v_P} = \sqrt{\frac{0.05(0.95)}{2142} + \frac{0.17(0.83)}{1055}} = 0.0125[/tex]
The standard error is of 0.0125.
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