. 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

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:

[tex]P(X = r) = nCr * p^{r} * (1 - p)^{n - r}[/tex]

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.

The blood bank at a hospital has 1,200 units of blood, out of which 37% units are of blood group B+. A clinical researcher randomly selects 300 units of blood and finds that 33% of those are of blood group B+. To test his result, he randomly selects 200 units of blood and finds that 40% of those are of blood group B+. Which of the following is the reason there is a difference between the two percentages selected by the researcher?

does y vary directly with x? if it does write an equation for the direct variation.

Y=1/3x-4 + Y=-7/3x+4

What is the area of a triangle with a base of √10 and a height of √13 Will mark brainliest

Find the amount of an annuity that consists of 25 quarterly payments of $800 each into an account that pays 8% interest per year, compounded quarterly. (Round your answer to the nearest cent.)

write as an expression: Fifteen more than the quotient of 24 and a number x. then evaluate when x equals 8

Which choice is equivalent to the product below?
v2.58
O A. 4./20
O B. 4/5
O C. 16.15
O D. 8/10

In the figure below, AABC is similar to A EFG. What is the length of EG? Enter only the number.
A
5
N
3
12
16
F
G
B
The solution is

A painter uses 15 gallons of interior paint to cover 300 square yards of wall and ceiling space. On a different job, he uses 8 gallons to cover 160 square yards. No paint is left over on either job. How many gallons of paint are needed to cover 1 square yard?​

slope 1/4 y-intercept 3 step by step

A coin is tossed and the spinner is spun one possible outcome is H3 (heads, 3). What is the sample space for the experiment?

what is 0.128 as a fraction​

Help I need the answers ASAP

PERSON WHO GETS RIGHT ILL GIVE BRAINLIEST! Which values from the given replacement set make up the solution set of this inequality? 3s>12; {4, 5, 6, 7}


{4}

{4, 5, 6}

{4, 5}

{5, 6, 7}

You are delt 1 card from a 52 card deck. Find the probability that you are not dealt a 10

twin oaks soccer field is a rectangle. The longer side of the field is 108 yards long. The shorter side is 56 yards long. What is the perimeter of the field?

A six-sided, fair number cube is rolled 100 times as part of an experiment. The frequency of the roll of the number 3 is 20. Which statement about rolling a 3 is correct?

The theoretical probability is 1/6. The experimental probability is 1/6.
The theoretical probability is 1/5. The experimental probability is 1/6.
The theoretical probability is 1/6. The experimental probability is 1/5.
The theoretical probability is 1/5. The experimental probability is 1/5.

In 2000, the moose population in a park was measured to be 650. By 2010, the population was measured to be 750. Assume the population continues to change exponentially. Find a formula for the moose population, P(x), where x is the number of years after 2000

29 divided by 6 eeeeeeeeeeeee

If .60 = N could you write the expression .60N

13. This shows a part of a multiplication table. Find the missing numbers. Explain how you found the numbers.

35 40
42 ?
? ?​

what is 3 1/3 - 1 1/2​

-4x +8 = 24
What is the value of x in the equation?
8
4
-4
-8

Melanie was training for a race. The line plot below shows the number of miles Melanie ran last week.


4. What does ¾ + ¼ = ?

Answer in simplest form.

6x + 34x - 6 =8(5x + 10)

In developing an interval estimate of the population mean, if the population standard deviation is unknown _____.

Maria is riding her bike through the Red Rock Loop. Maria recorded her distance traveled at five different
points during her bike ride. The table of values below shows the results of her bike ride.

Find the diameter of a circle with a circumference of 34.54 yards. Use 3.14 for π.

On a basketball court the free throw line is marked off geometrically this area of the court is called a key and is topped
by a semi circle that has a diameter of 12 feet find the arc length of the semi circle to the nearest foot find the area of a semi circle to the nearest square foot

a painter has 3 gallons of paint and each will cover 420 ft of wall space. if the total area was 1800 ft what percent of the job could the painter finish with the paint he already has?