Answer:
C. z = 2.05
Step-by-step explanation:
We have to calculate the test statistic for a test for the diference between proportions.
The sample 1 (year 1995), of size n1=4276 has a proportion of p1=0.384.
![p_1=X_1/n_1=1642/4276=0.384](https://tex.z-dn.net/?f=p_1%3DX_1%2Fn_1%3D1642%2F4276%3D0.384)
The sample 2 (year 2010), of size n2=3908 has a proportion of p2=0.3621.
![p_2=X_2/n_2=1415/3908=0.3621](https://tex.z-dn.net/?f=p_2%3DX_2%2Fn_2%3D1415%2F3908%3D0.3621)
The difference between proportions is (p1-p2)=0.0219.
The pooled proportion, needed to calculate the standard error, is:
![p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{1642+1415}{4276+3908}=\dfrac{3057}{8184}=0.3735](https://tex.z-dn.net/?f=p%3D%5Cdfrac%7BX_1%2BX_2%7D%7Bn_1%2Bn_2%7D%3D%5Cdfrac%7B1642%2B1415%7D%7B4276%2B3908%7D%3D%5Cdfrac%7B3057%7D%7B8184%7D%3D0.3735)
The estimated standard error of the difference between means is computed using the formula:
![s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.3735*0.6265}{4276}+\dfrac{0.3735*0.6265}{3908}}\\\\\\s_{p1-p2}=\sqrt{0.00005+0.00006}=\sqrt{0.00011}=0.0107](https://tex.z-dn.net/?f=s_%7Bp1-p2%7D%3D%5Csqrt%7B%5Cdfrac%7Bp%281-p%29%7D%7Bn_1%7D%2B%5Cdfrac%7Bp%281-p%29%7D%7Bn_2%7D%7D%3D%5Csqrt%7B%5Cdfrac%7B0.3735%2A0.6265%7D%7B4276%7D%2B%5Cdfrac%7B0.3735%2A0.6265%7D%7B3908%7D%7D%5C%5C%5C%5C%5C%5Cs_%7Bp1-p2%7D%3D%5Csqrt%7B0.00005%2B0.00006%7D%3D%5Csqrt%7B0.00011%7D%3D0.0107)
Then, we can calculate the z-statistic as:
![z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{0.0219-0}{0.0107}=\dfrac{0.0219}{0.0107}=2.05](https://tex.z-dn.net/?f=z%3D%5Cdfrac%7Bp_d-%28%5Cpi_1-%5Cpi_2%29%7D%7Bs_%7Bp1-p2%7D%7D%3D%5Cdfrac%7B0.0219-0%7D%7B0.0107%7D%3D%5Cdfrac%7B0.0219%7D%7B0.0107%7D%3D2.05)
z=2.05
30 students
14 have no siblings
that leaves 16 with siblings
6 have brothers and 12 have sisters which = 18 so 2 of the students have both a brother and a sister
2/30 students have a brother and a sister
1/15 chance
Answer:
4 45/100 Keep simplifying it. You can do it!
Step-by-step explanation:
4 is the whole. 45 is out of 100
Answer: just add 75 and 45 + x and do division for 69 ok but times the 45 with 69 ok good luck
Step-by-step explanation: