#12 **Statistical Analysis of Air Bag Vehicles in Fatal Auto Accidents****Problem Statement:**Researchers at VCU studied fatal auto accidents between cars in which one has an air bag and the other does not. They found that in 73% of all such fatal crashes, the driver of the air bag vehicle was responsible for the accident. Suppose that you obtain police records of fatal auto accidents. A random sample of 41 such accidents showed that 33 were the fault of the driver of the air bag vehicle. Does this indicate that the population proportion of such accidents in which the driver of the air bag vehicle was at fault is higher than 73%? Use a 5% level of significance.**Step-by-Step Solution:****a. State the hypotheses:**\[\text{H}_0: p = 0.73\] \[\text{H}_1: p > 0.73\]**b. Identify the level of significance and the critical value:**\[\alpha = 0.05\]\[z_0 = \text{from standard normal distribution for a one-tailed test at } \alpha = 0.05\]**c. Calculate the test statistic (z):**The test statistic is calculated using the formula:\[z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1 - p_0)}{n}}}\]Where:\[\hat{p} = \frac{33}{41}\]\[p_0 = 0.73\]\[n = 41\]**d. Calculate the p-value:**\[P = \text{P(Z > z)} \] **e. Decision:**Compare the calculated p-value with the significance level (α):- If $P \leq \alpha$, reject the null hypothesis, H0.- If $P > \alpha$, fail to reject the null hypothesis, H0._z-Score Formula:_\[z = \frac{X - \mu}{\sigma}\]_or_\[z = \frac{\bar{X} - \mu}{\frac{\sigma}{\sqrt{n}}}\]_End of Problem_This statistical procedure helps determine whether the proportion of drivers at fault in fatal auto accidents involving air bag vehicles is statistically significantly higher than 73%.

Name: #12 **Statistical Analysis of Air Bag Vehicles in Fatal Auto Accidents
Uploaded: 2024-03-05T11:52:21.000Z
Channel: Bartleby
Description: #12 **Statistical Analysis of Air Bag Vehicles in Fatal Auto Accidents****Problem Statement:**Researchers at VCU studied fatal auto accidents between cars in which one has an air bag and the other does not. They found that in 73% of all such fatal cr

Answered: Image /qna-images/answer/cfe4e8fa-209c-4edb-bbe1-ce1031a0d574.jpg

Math

Statistics

12. Researchers at VCU studied fatal auto accidents between cars in which one has an air bag and the other does not. They found that in 73% of all such fatal crashes the driver of the air bag vehicle was responsible for the accident. Suppose that you obtain police records of fatal auto accidents. A random sample of 41 such accidents showed that 33 were the fault of the driver of the air bag vehicle. Does this indicate that the population proportion of such accidents in which the driver of the air bag vehicle was at fault is higher than 73%? Use a 5% level of significance.

12. Researchers at VCU studied fatal auto accidents between cars in which one has an air bag and the other does not. They found that in 73% of all such fatal crashes the driver of the air bag vehicle was responsible for the accident. Suppose that you obtain police records of fatal auto accidents. A random sample of 41 such accidents showed that 33 were the fault of the driver of the air bag vehicle. Does this indicate that the population proportion of such accidents in which the driver of the air bag vehicle was at fault is higher than 73%? Use a 5% level of significance.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Q: 12 5 10

Q: a) How many students are taking Art?

A: the number of students taking Art if given by 6+10=16

Q: 4s +5 S -4

Q: (4) y=x +4 -5 -4 -3 6.

A: The given equation is: y=x+4

Q: What is the Probability that a student is not taking either class?

A: From the given Venn diagram, it is observed that the number of students who are taking art only is…

Q: a3-16a

A: a³−16a ⇒a(a²−16) ⇒a(a² −4²) ⇒a(a+4)(a−4)

Q: -7.4v+2.4(-7.1v+-10)+6.7

A: simplified value is -24.44 v - 17.3

Q: 2.3 Q13

A: The objective of this question is to use the Squeeze Theorem to show that the limit as x approaches…

Q: %3D n+1 3 -2 -3

Q: 1+7/7 + 8

A: Answar would be 10

Q: 5у 10y

A: Given, 5y/10y Cancelling y from both numerator and denominator to get, 5/10 Now, 5/10 can…

Q: (4 – a2)

A: To integrate.

Q: -8 - 12

A: Given problem is

Q: graph shows the relationship between the volume of the dilated box and the scale factor. diusuon 5.…

Q: S-4 a(5-35 +16

Q: 2x° 28 4y 28

Q: 5 L s² + 2s – 3

A: We know that, Laplace transform of 1/(s-1) = e^t

Q: 4. Fill in the following contingency table with the number of observations that fall into each com-…

A: x1 = number of colored oranges from Skittles brand = 77 x2 = number of colored oranges from M &…

Q: w + (-7), when w = - 1

A: The expression is given by w+(-7) To evaluate: The value of the expression when w=-1.

Q: 2+1+5+7

A: 2+1+5+7=3+5+7=15

Q: 1+4+6+8

Q: 12 30 24

Q: 11 4.

Q: 6. Using the data from the contingency table, obtain the value of the test statistic of our test. 7.…

A: Step 1: Given: x1 = number of colored oranges from Skittles brand = 77 x2 = number of colored…

Q: -4 -2- 4 8

A: We are asked to find the horizontal asymptote and vertical asymptote. Horizontal asymptote (HA) - It…

Q: -2 -4 and D = 4 8

Q: 9. x+8

A: For two intersecting chords , the multiples of the lengths of the line segments on each chord are…

Q: 6 1/6 + 6

Q: Two and two

A: Given: Two and two

Concept explainers

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.

Topic Video

Question

#12

**Statistical Analysis of Air Bag Vehicles in Fatal Auto Accidents**

**Problem Statement:**

Researchers at VCU studied fatal auto accidents between cars in which one has an air bag and the other does not. They found that in 73% of all such fatal crashes, the driver of the air bag vehicle was responsible for the accident. Suppose that you obtain police records of fatal auto accidents. A random sample of 41 such accidents showed that 33 were the fault of the driver of the air bag vehicle. Does this indicate that the population proportion of such accidents in which the driver of the air bag vehicle was at fault is higher than 73%? Use a 5% level of significance.

**Step-by-Step Solution:**

**a. State the hypotheses:**
\[\text{H}_0: p = 0.73\]
\[\text{H}_1: p > 0.73\]

**b. Identify the level of significance and the critical value:**
\[\alpha = 0.05\]
\[z_0 = \text{from standard normal distribution for a one-tailed test at } \alpha = 0.05\]

**c. Calculate the test statistic (z):**

The test statistic is calculated using the formula:
\[z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1 - p_0)}{n}}}\]

Where:
\[\hat{p} = \frac{33}{41}\]
\[p_0 = 0.73\]
\[n = 41\]

**d. Calculate the p-value:**
\[P = \text{P(Z > z)} \]

**e. Decision:**

Compare the calculated p-value with the significance level (α):

- If $P \leq \alpha$, reject the null hypothesis, H0.
- If $P > \alpha$, fail to reject the null hypothesis, H0.

_z-Score Formula:_
\[z = \frac{X - \mu}{\sigma}\]
_or_
\[z = \frac{\bar{X} - \mu}{\frac{\sigma}{\sqrt{n}}}\]

_End of Problem_

This statistical procedure helps determine whether the proportion of drivers at fault in fatal auto accidents involving air bag vehicles is statistically significantly higher than 73%.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Application of Algebra$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.

Similar questions

9+n=2
Solue for 4x²-16 z O
7 3/5 + 2/3
3 Group of 6
18+0.496+16.8
-1 2 5 2 7 -5 Let B = and C = 2 5 3 2 3 5 Find -4B+ 5C. >
7 20 21
1+1 w
(4x + 4, y) 2. 11 1 1 2. 2. 2. 2. 2. 111