Mathematics, 06.12.2019 05:31 tingzontumbler9061

Assume the population proportion is to be estimated from the sample described. find the approximate margin of error and the 95% confidence interval for the population proportion. sample size = 225, sample proportion = 0.28 the margin of error is 0.0587. (round to four decimal places as needed.) find the 95% confidence interval. (round to the three decimal places as needed.)

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Answer from: zazzles88151

We can conclude that the true population proportion at 95% of confidence is between (0.221;0.339)

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

$\hat p =0.28$ represent the estimated proportion for the sample

n=225 is the sample size required

represent the critical value for the margin of error

The population proportion have the following distribution

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

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.

$z_{\alpha/2}=1.96$

The margin of error is given by :

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

$Me=1.96 \sqrt{\frac{0.28(1-0.28)}{225}}=0.0587$

And replacing into the confidence interval formula we got:

$0.28 - 1.96 \sqrt{\frac{0.28(1-0.28)}{225}}=0.221$

$0.28 + 1.96 \sqrt{\frac{0.108(1-0.28)}{225}}=0.339$

And the 95% confidence interval would be given (0.221;0.339).

We can conclude that the true population proportion at 95% of confidence is between (0.221;0.339)

Answer from: Quest

answer: plz give a pic and answer choices so i can answer!

step-by-step explanation:

Answer from: Quest

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.