1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
PIT_PIT [208]
2 years ago
7

. In a study of air-bag effectiveness it was found that in 821 crashes of midsize cars equipped with air bags, 46 of the crashes

resulted in hospitalization of the drivers (based on data from the highway Loss Data Institute). Using a 0.01 significance level, you need to test the claim that the air-bag hospitalization rate is lower than the 7.8% rate for crashes of mid-size cars equipped with automatic safety belts. What conclusion should you make
Mathematics
1 answer:
jok3333 [9.3K]2 years ago
5 0

Answer:

P(X ≤ 46 | X~B(821, 0.078)) = 0.00885745584

0.00885... < 0.01

The test statistic of 46 is significant

There is sufficient evidence to reject H₀ and accept H₁

Air bags are more effective as protection than safety belts

Step-by-step explanation:

821 crashes

46 hospitalisations where car has air bags

7.8% or 0.078 probability of hospitalisations in cars with automatic safety belts

α = 0.01 or 1% ← level of significance

One-tailed test

We are testing whether hospitalisations in cars with air bags are less likely than in a car with automatic safety belts;

The likelihood of hospitalisation in a car with automatic safety belts, we are told, is 7.8% or 0.078;

So we are testing if hospitalisations in cars with air bags is less than 0.078;

So, firstly:

Let X be the continuous random variable, the number of hospitalisations from a car crash with equipped air bags

X~B(821, 0.078)

Null hypothesis (H₀): p = 0.078

Alternative hypothesis (H₁): p < 0.078

According to the information, we reject H₀ if:

P(X ≤ 46 | X~B(821, 0.078)) < 0.01

To find P(X ≤ 46) or equally P(X < 47), it could be quite long-winded to do manually for this particular scenario;

If you are interested, the manual process involves using the formula for every value of x up to and including 46, i.e. x = 0, x = 1, x = 2, etc. until x = 46, the formula is:

P(X = r) = nCr * p^{r}  * (1 - p)^{n - r}

You can find binomial distribution calculators online, where you input n (i.e. the number of trials or 821 in this case), probability (i.e. 0.078) and the test statistic (i.e. 46), it does it all for you, which gives:

P(X ≤ 46 | X~B(821, 0.078)) = 0.00885745584

Now, we need to consider if the condition for rejecting H₀ is met and recognise that:

0.00885... < 0.01

There is sufficient evidence to reject H₀ and accept H₁.

To explain what this means:

The test statistic of 46 is significant according to the 1% significance level, meaning the likelihood that only 46 hospitalisations are seen in car crashes with air bags in the car as compared to the expected number in car crashes with automatic safety belts is very unlikely, less than 1%, to be simply down to chance;

In other words, there is 99%+ probability that the lower number of hospitalisations in car crashes with air bags is due to some reason, such as air bags being more effective as a protective implement than the safety belts in car crashes.

You might be interested in
What is the answer?
Tresset [83]
The standard eqn of a parabola in vertex form is y-k = a(x-h)^2, where (h,k) is the vertex.  There are a good number of steps involved.  I don't think it wise not to "show work."  I cannot answer this question without going through all those steps.

However, there's an easier way to find the vertex.  Identify the coefficients a, b and c:

a= -4, b= -3 and c = 1

Then the x-coord. of the vertex is x = -b / (2a).  Subst. -3 for b and -4 for a and simplify.  x = ??

Then find the y-coord. of the vertex by subbing your result, above, into the original equation. 

Write the vertex as (h,k).

Once you have this vertex, you can find the equation in vertex form as follows:

Start with the general form y-k = a(x-h)^2, where (h,k) is the vertex.

You've already found the vertex (h,k).  Subst. h and k into the general form, above.  Then only the coefficient "a" remains undefined.
5 0
3 years ago
What do the terms "mins" and "maxs" represent? uhaul?
Talja [164]
When it comes to parabolas, minimum is the vertex for the graph if it opens up (a term is +) and maximum is the vertex for the graph if it opens down (a term is -).
5 0
3 years ago
Solve for z.<br><br> x + y + z = 4<br><br> 4x - y - z = 1<br><br> x + z = 2
AleksAgata [21]

Answer:

z= 4-x-y

z= -1+4x-y

z= 2-x

8 0
2 years ago
Read 2 more answers
Please help! picture above plus, part B: write the quadratic expression in the numerator and the dominator in factored form. Par
Dennis_Churaev [7]

Answer:

work is shown and pictured

7 0
3 years ago
Read 2 more answers
Correct I’ll give brainlist no links or I’ll report
Elenna [48]

Since he started with Nothing

He had zero initially

After x Months...

He'll have 10x naxvips

in slope intercept form

y=10x

To get the y values ... substitute the corresponding x value

For x=0

y=10(0)

y=0. Which is true cos he had no naxvip initially

x=1

y=10(1)

=10. Which is true cos he buys 10 more monthly... So 10 + 0 = 10.

x=2

y=10(2) = 20. This is true cos he added an additional 10 after each month

x=7

y=70.

8 0
2 years ago
Other questions:
  • The owner of a garden center pays $12 for each birdbath. She sells them for 55% more than she paid. Decide whether each expressi
    7·1 answer
  • The picture shows a barn door:
    15·1 answer
  • What is the solution set for x 2 + 6 x + 10 = 0 ?
    15·1 answer
  • If you could travel 450 miles in 5.5 hours, then how far could you travel in 7 hours?​
    6·1 answer
  • If Tara spends $219 a month for her car payment and she makes $3200 a month what percent of her monthly income is spent on her c
    13·1 answer
  • Red 13 Silver 34 Black 25 White 10 Blue 8
    13·2 answers
  • Which of these is an example of physical change?
    11·1 answer
  • Given that AB = 370 m and AC = 510 m, find
    13·1 answer
  • What is the general equation of a sine function with an amplitude of 2, a period of Pi and a horizontal shift of Pi units? y = 2
    15·1 answer
  • A mother is 25 years older than her son. <br>Write down the son's age and the mother's age<br>​
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!