Can anyone help me with this and explain it too?

Mathematics

1 answer:

arlik [135]3 years ago

7 0

Answer:

(6, 3)

Step-by-step explanation:

$Midpoint (x_{m},y_{m})=(\frac{x_A + x_B}{2}, \frac{y_A + y_B}{2})\\\\=(\frac{3 + 9}{2}, \frac{6 + 0}{2})\\\\=(\frac{12}{2}, \frac{6}{2})\\\\Midpoint of a line segment (x_M, y_M) = (6, 3)$

How to Calculate Midpoint?

The x-coordinate of the midpoint M of the segment $\overline{AB}$ is the arithmetic mean of the x-coordinates of the endpoints of the segment $\overline{AB}$ . Similarly, the y-coordinate of the midpoint M of the segment $\overline{AB}$ is the arithmetic mean of the y-coordinates of the endpoints of the segment $\overline{AB}$ .

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A candidate for one of Ohio's two U.S. Senate seats wishes to compare her support among registered voters in the northern half o

Radda [10]

Answer:

$(0.531-0.45) - 1.96 \sqrt{\frac{0.531(1-0.531)}{2000} +\frac{0.45(1-0.45)}{2000}}=0.050$

$(0.531-0.45) + 1.96 \sqrt{\frac{0.531(1-0.531)}{2000} +\frac{0.45(1-0.45)}{2000}}=0.112$

And the best option for this case would be:

A. 0.050 to 0.112.

Step-by-step explanation:

Data given

$p_A$ represent the real population proportion of who support the cnadite for the northern half state

$\hat p_A =\frac{1062}{2000}=0.531$ represent the estimated proportion of who support the candidate for the northern half state

$n_A=2000$ is the sample size required the northern half state

$p_B$ represent the real population proportion of who support the candidate for the southern half state

$\hat p_B =\frac{900}{2000}=0.45$ represent the estimated proportion of people who support the candidate for the southern half state

$n_B=2000$ is the sample size for the northern half state

$z$ represent the critical value

The confidence interval for the difference of two proportions would be given by this formula

$(\hat p_A -\hat p_B) \pm z_{\alpha/2} \sqrt{\frac{\hat p_A(1-\hat p_A)}{n_A} +\frac{\hat p_B (1-\hat p_B)}{n_B}}$

For the 95% confidence interval the value of $\alpha=1-0.95=0.05$ and $\alpha/2=0.025$ , with that value we can find the quantile in the normal standard distribution and we got.