Mathematics, 04.04.2020 11:46 kat9940

An environmental agency worries that many cars may be violating clean air emissions standards. The agency hopes to check a sample of vehicles in order to estimate that percentage with a margin of error of 55% and 9090% confidence. To gauge the size of the problem, the agency first picks 7070 cars and finds 1414 with faulty emissions systems. How many should be sampled for a full investigation?

Answers: 1

Show answers

Answers

Answer from: admierewebb

$n=\frac{0.2(1-0.2)}{(\frac{0.05}{1.64})^2}=172.13$

And rounded up we have that n=173

Step-by-step explanation:

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".

represent the real population proportion of interest

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

n is the sample size required (variable of interest)

represent the critical value for the margin of error

Solution to the problem

The population proportion have the following distribution

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

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 $\alpha=1-0.90=0.10$ and $\alpha/2 =0.05$ . And the critical value would be given by:

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

The margin of error for the proportion interval is given by this formula:

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

And on this case we have that $ME =\pm 0.05$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

We can assume that the estimates proportion is $\hat p=\frac{14}{70}=0.2$ . And replacing into equation (b) the values from part a we got:

$n=\frac{0.2(1-0.2)}{(\frac{0.05}{1.64})^2}=172.13$

And rounded up we have that n=173

Answer from: Quest

B-simple yes/no questions

Answer from: Quest

first, you divide the triangle in two, tô form a retangle triangle. after, using pythagoream theorem:

18^2 = 14^2 + (x/2)^2

(x^2/4) + 196 = 324

x^2/4 = 324 - 196

x^2/4 = 128

x^2 = 512

x = √512

x = √2^9

x = 16√2 cm

i hope i you.

Another question on Mathematics

Mathematics, 21.06.2019 20:20

Aline passes through (1,-5) and(-3,7) write an equation for the line in point slope form rewrite the equation in slope intercept form

Answers: 1

Answer

Mathematics, 21.06.2019 20:30

Jason went to an arcade to play video games. he paid $2 for every 11 tokens he bought. he spent a total of $16 on tokens. which equation can be used to determine,t, the number lf tokens jason bought

Answers: 1

Answer

Mathematics, 21.06.2019 23:30

The area (a) of a circle with a radius of r is given by the formula and its diameter (d) is given by d=2r. arrange the equations in the correct sequence to rewrite the formula for diameter in terms of the area of the circle.

Answers: 1

Answer

Mathematics, 22.06.2019 01:30

What rule describes a dilation with a scale factor of 4 and the center of dilation at the origin?

Answers: 2

Answer

You know the right answer?

An environmental agency worries that many cars may be violating clean air emissions standards. The a...

Questions