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
Which measurement is greater:640 ft or 0.5 mi
hammer [34]

Answer:

0.5 mi (2640 feet)

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
Wich is greater 8kg or 30 oz
Anna11 [10]
8kg, Because 8kg in oz is 282
5 0
3 years ago
Read 2 more answers
HELP ASAP!!! select all the descriptions that apply to the transformation!
maxonik [38]

Answer: A and B

Step-by-step explanation:

The shape is moving from right to left and down

6 0
2 years ago
. A group of 18 people ordered soup and sandwiches for
larisa [96]

its 18 because if u add 18 to 34



7 0
3 years ago
Segment KJ shown below is the hypotenuse of isosceles right triangle JLK.
irga5000 [103]
On a coordinate plane it is negetive 5
7 0
2 years ago
Read 2 more answers
Other questions:
  • Admission for a movie is $8 for children and $12 for adults. On a certain day, 3200 people attend the movie theater and $33,040
    14·1 answer
  • If the length football field is 100 yards and the width is 53.3 yards, what is the area?
    7·2 answers
  • A cylinder has a volume of 72 cubic inches. What iis the volume of a cone with the same height and radius as the cylinder?
    10·1 answer
  • Find the product. (-2x^2 )^3 ·3 x
    5·2 answers
  • Idk how to do #6. someone help
    14·1 answer
  • Assume markup is based on selling price. Solve for the selling price
    10·2 answers
  • Describe a transformation or series of transformations that demonstrates the congruence between figures A and B.
    13·1 answer
  • The Pete meter of a rectangle with a length of 10 cm is 31 cm What is the width of the rectangle?
    5·1 answer
  • Quel est le rayon d'une demi-boule ayant un volume de 248,832 pie décimètres cubes ?
    14·1 answer
  • Write the equation of the line that passes through the points (2, -6) and (8, -2).
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!