Mathematics, 19.03.2020 23:15 YoungManAlex

"Calculate a 90% confidence interval for the proportion of Americans who decide to not go to college because they cannot afford it, and interpret the interval in context. Round to 4 decimal places."

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Answer from: ayoismeisjuam

$0.48 - 1.64\sqrt{\frac{0.48(1-0.48)}{331}}=0.435$

$0.48 + 1.64\sqrt{\frac{0.48(1-0.48)}{331}}=0.525$

The 90% confidence interval would be given by (0.435;0.525)

Step-by-step explanation:

Assuming this previous info: "Exercise 6.16 presents the results of a poll where 48% of 331 Americans who decide to not go to college do so because they cannot afford it".

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

The estimated proportion for this case is 0.48 and n = 331

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 90% of confidence, our significance level would be given by $\alpha=1-0.90=0.1$ and $\alpha/2 =0.05$ . And the critical value would be given by:

$t_{\alpha/2}=-1.64, t_{1-\alpha/2}=1.64$

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:

$0.48 - 1.64\sqrt{\frac{0.48(1-0.48)}{331}}=0.435$

$0.48 + 1.64\sqrt{\frac{0.48(1-0.48)}{331}}=0.525$

The 90% confidence interval would be given by (0.435;0.525)

Answer from: Quest

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

$m\angle qrt=156^o$

$m\angle qst=156^o$

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.

Answer from: Quest

i think it would be c

mark brainliest if im right

step-by-step explanation:

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