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

135 is your answer

step-by-step explanation:

try 180 times three then divide that number by 4 (sides) to get your answer. im glad to : )

Answer from: Quest

d. millimeters per hour.

step-by-step explanation:

we are given that,

carlo used a rain gauge to measure the amount of water his lawn is receiving from the sprinklers.

since, according to the options, we see that,

water cannot be measured by 'miles per hour', 'meters per second' and 'grams per seconds'.

we get that, the water can be measured by 'millimeters per hour'.

hence, the appropriate rate for describing the amount of water is 'millimeters per hour'.

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