PLEASE HELP 7TH GRADE MATH

Suppose that insurance companies did a survey. They randomly surveyed 400 drivers and found that 320 claimed they always buckle

nirvana33 [79]

Answer:

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

And replacing we got:

$ME= 1.96*\sqrt{\frac{0.8 (1-0.8)}{400}} =0.0392$

ii) $Lower = 0.8-0.0392= 0.7608$

$Upper = 0.8 +0.0392= 0.8392$

Step-by-step explanation:

Notation and definitions

$X=320$ number of people that claimed always buckle up.

$n=400$ random sample taken

$\hat p=\frac{320}{400}=0.8$ estimated proportion of people that claimed always buckle up

$p$ true population proportion of people that claimed always buckle up

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

Part i

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 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by:

$z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96$

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

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

The margin of error is given by:

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

And replacing we got:

$ME= 1.96*\sqrt{\frac{0.8 (1-0.8)}{400}} =0.0392$

Part ii

And the confidence interval would be given by:

$Lower = 0.8-0.0392= 0.7608$

$Upper = 0.8 +0.0392= 0.8392$

6 0

2 years ago

What is the greatest common factor of 14 and 22

Alecsey [184]

Answer:

2

Step-by-step explanation:

greatest common factor means the greatest number we can divide by for each of the number and still get a whole number

14 and 22. they are both even so one factor is 2

if we check, 14 & 22 aren't both divisible by 3,4,5,6,7,8,9,10,11,12,13,14 so the gcf is 2

4 0

3 years ago

Read 2 more answers

Samuel, a county social worker, helps county residents who are struggling with different issues. He uses “c” to indicate client

Nadya [2.5K]

Answer:

70%

Step-by-step explanation:

Out of 7+3 = 10 total hours Samuel logged on Thursday, 7 were spent with clients. The fraction of hours spent with clients was ...

client hours / total hours = 7/10

Multiplying by 100% converts that to a percentage:

Thursday client time = 7/10 × 100% = 70%

3 0

2 years ago

Which of these lines could possibly intersect the graph of a function at more than one point? Select three that apply.

Vera_Pavlovna [14]

According to Vertical Line test, a vertical line only intersect the graph of a function at one point. Among the choices given, x = 4 is a vertical line. So this line cannot intersect the graph of a function at more than one point. The other three would apply. So the answer choices are A, C and D.

8 0

3 years ago

Please help answer thisq

Julli [10]

Answer:

More than one independent variable being tested.

Step-by-step explanation:

If a student wants to figure out if ONLY salt affects the growth of seeds, the student shouldn't change the amount of sunlight being received.

5 0

2 years ago