Mathematics, 06.03.2020 19:32 mackenziemelton26

Suppose the survey was based on a sample of 700 companies. Find the 80% confidence interval for the proportion of all companies likely to require higher employee contributions for health care coverage. Find the LEFT endpoint and RIGHT endpoint.

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Answer from: MrKrinkle77

$0.61 - 1.28\sqrt{\frac{0.61(1-0.61)}{700}}=0.586$

$0.61 + 1.28\sqrt{\frac{0.61(1-0.61)}{700}}=0.634$

The 80% confidence interval would be given by (0.586;0.634)

Step-by-step explanation:

A recent survey showed that 61% of U.S. employers were likely to require higher employee contributions for health care coverage. Suppose the survey was based on a sample of 700 companies. Find the 80% confidence interval for the proportion of all companies likely to require higher employee contributions for health care coverage.

Previous concepts

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".

The population proportion have the following distribution

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

Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 80% of confidence, our significance level would be given by $\alpha=1-0.80=0.2$ and $\alpha/2 =0.1$ . And the critical value would be given by:

$z_{\alpha/2}=-1.28, z_{1-\alpha/2}=1.28$

The confidence interval for the mean is given by the following formula:

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

If we replace the values obtained we got:

$0.61 - 1.28\sqrt{\frac{0.61(1-0.61)}{700}}=0.586$

$0.61 + 1.28\sqrt{\frac{0.61(1-0.61)}{700}}=0.634$

The 80% confidence interval would be given by (0.586;0.634)

Answer from: Quest

x = 10.1

step-by-step explanation:

all of the angles of a tirangle add up to 180º

180 - 65 = 115 (since we already know the value of one angle)

(2x + 7) + (8x + 7) = 115

(combins like terms) 10x + 14 = 115

(isolate the variable subtract 14 from both sides): 10x = 101

(find the variable divide both sides by 10): x = 101/10

x = 10.1

Answer from: Quest

instagram is better than go there instead lol

step-by-step explanation:

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