MATHEMATICS COLLEGE

. 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

Answers

Answer 1

Answer:

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.

Related Questions

On the package for a certain brand of spinach seeds there is a guarantee that, if the printed instructions are followed, of planted seeds will germinate. A random sample of seeds is chosen. If these seeds are planted according to the instructions, find the probability that of them germinate.
Find the area of the right triangle.
-2a+5b-7-5a+b-4 please help lol
Find the solution of the system of equations . - 5x + 9y = 11 x - 3y = - 7how do i solve this
What is the median for the set of data shown below?16, 23, 24, 39, 45, 78, 95

a moving truck charges $250 to rent a truck and $0.40 for each mile driven. mr.lee paid a total of $314. which equation can be used to find m, the number of miles he drove the moving truck?

Answers

(314 - 250) / 0.40 = m
^divided by
m = 160

m=160 I double checked

a discount voucher offering 15% off is used to pay a bill. after using the voucher the bill is reduced to 36.72. how much was the bill before applying the voucher discount

Answers

We can use the is/of=p/100 method for this problem. Since it's 15% off, this would mean that the bill is 85% of what it was initially. Plug the values into the is/of=p/100 formula.

36.72/x = 85/100

Solve for x.

x=36.72/0.85

x=43.2

So, the bill was $43.20 before applying the voucher discount of 15% off.

The answer is 244.80

You can calculate this by taking 36.72 and dividing it by 0.15 (15%). You would do this because it is the opposite of multiplying an original number by 0.15 (15%) to get 36.72.

Hope It helps!

Please vote Brainliest!

A trainee examined a set of experimental data to find comparisons that "look promising" and calculated a family of Bonferroni confidence intervals for these comparisons with a 90 percent family confidence coefficient. Upon being informed that the Bonferroni procedure is not applicable in this case because the comparisons had been suggested by the data, the trainee stated:"This makes no difference. I would use the same formulas for the point estimates and the estimated standard errors even if the comparisons were not suggested by the data." Please disscuss.

Answers

Answer:

Answer for the question:

Please disscuss.

Is explained in the attachment.

Step-by-step explanation:

Final answer:

The trainee's assertion is flawed as the Bonferroni method's assumption of independence doesn't hold when comparisons are derived from the data. For a smaller error bound at the same confidence level, sample size should be increased before the study. Moreover, reliance on null hypothesis significance testing can be problematic, and alternative evidence estimation methods may be more informative.

Explanation:

The trainee's use of Bonferroni confidence intervals with a 90 percent family confidence coefficient assumes independent comparisons. However, when comparisons are suggested by the data, the assumption of independence is violated, rendering the Bonferroni method inappropriate. The trainee errs by stating that using the same formulas for point estimates and estimated standard errors would not differ in the other scenario. When comparisons are data-derived, adjustments such as using resampling methods or adjusting for multiple testing should be considered to account for the increased risk of Type I error.

Regarding the desire for a smaller error bound while keeping the same level of confidence, one should increase the sample size of the study before it is conducted. This would enable a more precise estimate with a narrower confidence interval without altering the confidence level.

To avoid the limitations of null hypothesis significance testing (NHST), alternative approaches such as estimation of evidence strength through model comparison criteria like AIC or BIC, or using Bayesian methods, might be employed. These do not rely on arbitrary significance thresholds and often provide a more informative assessment of model's evidential support.

Learn more about Statistical Significance here:

brainly.com/question/33838241

#SPJ3

4x<-2 como se desarrolla esta desigualdad

Answers

Answer:

x<-0.5

Step-by-step explanation:

Help!!!

prove triangle PAB is an equilateral triangle

HELP PLEASEE

Answers

Answer:

If three sides of a triangle are equal and the measure of all three angles is equal to 60 degrees then the triangle is an equilateral triangle. Therefore it is an equilateral triangle.

In ∆PAM and ∆PBM

$\because\pink{\sf\begin{cases} \sf AM=BM(Bisected\:by\:PM)\n \sf PA=PB(Given)\n \sf PM(Common\:side)\end{cases}}$