Mathematics, 06.12.2019 06:31 hemolelekeakua

1. the town of hayward (california) has about 50,000 registered voters. a political scientist takes a simple random sample of 500 of these voters. in the sample, the breakdown by party affiliation is republican 115 democrat 331 independent 54
the range from to is a 95% confidence interval for the percentage of independents among fill in the first two blanks with numbers. fill in the last blank with one of the following two options: "all the 50,000 voters in the population", "500 voters in the sample".

Answers: 1

Show answers

Answers

The range from 8.08% to 13.52% is a 95% confidence interval for the percentage of independents among the 50000 registered votersof the town of Hayward

Step-by-step explanation:

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".

represent the real population proportion of interest

$\hat p =\frac{54}{500}=0.108$ represent the estimated proportion for the sample of independents

n=500 is the sample size required (variable of interest)

represent the critical value for the margin of error

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})$

The confidence interval would be given by this formula

$\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

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 required for the interval in the normal standard distribution.

$z_{\alpha/2}=1.96$

And replacing into the confidence interval formula we got:

$0.108 - 1.96 \sqrt{\frac{0.108(1-0.108)}{500}}=0.0808$

$0.108 + 1.96 \sqrt{\frac{0.108(1-0.108)}{500}}=0.1352$

And the 95% confidence interval would be given (0.0808;0.1352).

The range from 8.08% to 13.52% is a 95% confidence interval for the percentage of independents among the 50000 registered votersof the town of Hayward

Answer from: Quest

the system of inequity is

$y\leq -x+4$

$3y> x$

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

the solid line passing through the points (0,4) and (4,0).

$y-4=\frac{0-4}{4-0}(x-0)$

$y=-x+4$

the related equation of solid line is $y=-x+4$ .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

$y-0=\frac{0-1}{3-0}(x-0)$

$3y=x$

the related equation of dashed line is $3y=x$

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

$1=-0+4$

$1=4$

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be $\leq$ . the required inequality is