Mathematics, 17.12.2019 04:31 india73

G"motor vehicle accidents are rare events, but it is always better to have fewer. vehicle speed may be related to the number of accidents, and in general it is believed that slower speeds will lead to fewer accidents. on a stretch of highway 42, the average number of accidents per day was 0.23. a month ago, the speed limit was changed from 60 miles per hour to 50 miles per hour. in the one month period following the change in the speed limit, three accidents were observed. explain in detail how you would test whether this is a significant decrease (3pts). include a description of your null and alternative hypotheses."

Answers: 3

Show answers

Answers

Answer from: cmg27

To test wether this is a significant decrease we have to perform a hypothesis test on the proportions.

The null hypothesis represents the past condition (the proportion of 0.23 accidents/day is equal or bigger) and the alternative hypothesis is what we claim that is happening now (the proportion have lowered).

We want to perform the test in order to know if there is enough evidence that it has changed. The result can be:

- The null hypothesis is rejected: there is enough evidence with this sample that the rate of accidents has lowered from 0.23.

- The null hypothesis failed to be rejected: there is not enough evidence to say that the rate of accidents has lowered, although the sample proportion is lower.

Step-by-step explanation:

Numerical solution:

We have to perform a hypothesis test on proportions. We want to know if there is enough evidence to claim that the number of accidents per day has lowered from 0.23.

The null and alternative hypothesis are:

$H_0: \pi\geq0.23\\\\H_1:\pi$

The significance level assumed is 0.05.

The proportion of the sample is:

$p=\frac{3}{30}=0.1$

The standard deviation is calculated from the population proportion

$\sigma=\sqrt{\pi(1-\pi)/N} =\sqrt{0.23*(1-0.23)/30} =0.077$

The z-value now can be calculated as

$z=\frac{p-\pi+0.5/N}{\sigma}=\frac{0.10-0.23+0.5/30}{0.077} =-1.475$

The P-value for z=-1.475 is P=0.07011. The P-value is greater than the significant level, so the effect is not significant and it failed to reject the null hypothesis.

Answer from: Quest

the system of inequity is

$y\leq -x+4$

$3y> x$

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

the solid line passing through the points (0,4) and (4,0).

$y-4=\frac{0-4}{4-0}(x-0)$

$y=-x+4$

the related equation of solid line is $y=-x+4$ .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

$y-0=\frac{0-1}{3-0}(x-0)$

$3y=x$

the related equation of dashed line is $3y=x$

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

$1=-0+4$

$1=4$

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be $\leq$ . the required inequality is

$y\leq -x+4$

similarly, check the second related equation.

$3(1)=0$

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is

$3y> x$

15 points write a system of inequalities to represent the shaded portion of the graph

Answer from: Quest

step-by-step explanation:

because that's the answer

The stem-and-leaf plot above lists the number of ingredients found in different industrial cleaners.

Another question on Mathematics

Mathematics, 21.06.2019 13:30

What is the exact volume of the cylinder (radius 13 in., height 30 in.)

Answers: 1

Answer

Mathematics, 21.06.2019 13:30

Find two rational expressions that have the difference of 2-n/n-4

Answers: 1

Answer

Mathematics, 21.06.2019 15:10

Point a is located at (0, 4), and point c is located at (−3, 5). find the x value for the point b that is located one fourth the distance from point a to point c. −0.25 −0.5 −0.75 −1

Answers: 1

Answer

Mathematics, 21.06.2019 16:50

What are the steps to solving the inequality 3b + 8 ≥ 14?

Answers: 1

Answer

You know the right answer?

G"motor vehicle accidents are rare events, but it is always better to have fewer. vehicle speed may...

Questions