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
spayn [35]
3 years ago
11

2. The National Safety Council routinely analyzes the benefit of seat belt use on driver safety. Their data showed that among 28

23 drivers not wearing seat belts, 31 died as a result of injuries, and among 7765 drivers wearing seat belts 16 were killed. Test the hypothesis (at 95% confidence) that there is no difference in the proportion of deaths between the 2 groups. What do you conclude? Calculate the margin of error (E) at 95%.
Mathematics
1 answer:
JulijaS [17]3 years ago
5 0

Answer:

We conclude that there is difference in the proportion of deaths between the 2 groups.

Step-by-step explanation:

We are given that among 2823 drivers not wearing seat belts, 31 died as a result of injuries, and among 7765 drivers wearing seat belts 16 were killed.

Let p_1 = <u><em>proportion of deaths when drivers were not wearing seat belts.</em></u>

p_2 = <u><em>proportion of deaths when drivers were wearing seat belts.</em></u>

So, Null Hypothesis, H_0 : p_1=p_2      {means that there is no difference in the proportion of deaths between the 2 groups}

Alternate Hypothesis, H_A : p_1\neq p_2     {means that there is difference in the proportion of deaths between the 2 groups}

The test statistics that would be used here <u>Two-sample z test for proportions;</u>

                          T.S. =  \frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }  ~ N(0,1)

where, \hat p_1 = sample proportion of deaths when drivers were not wearing seat belts = \frac{31}{2823} = 0.011

\hat p_2 = sample proportion of deaths when drivers were wearing seat belts = \frac{16}{7765} = 0.002

n_1 = sample of drivers not wearing seat belts = 2823

n_2 = sample of drivers wearing seat belts = 7765

So, <u><em>the test statistics</em></u>  =  \frac{(0.011-0.002)-(0)}{\sqrt{\frac{0.011(1-0.011)}{2823}+\frac{0.002(1-0.002)}{7765} } }

                                       =  4.438

The value of z test statistics is 4.438.

<u>Now, at 5% significance level the z table gives critical values of -1.96 and 1.96 for two-tailed test.</u>

Since our test statistic doesn't lie within the range of critical values of z, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which <u>we reject our null hypothesis</u>.

Therefore, we conclude that there is difference in the proportion of deaths between the 2 groups.

Also, <u>Margin of error</u> (E) =  1.96 \times \sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} }

                                        =  1.96 \times \sqrt{\frac{0.011(1-0.011)}{2823}+\frac{0.002(1-0.002)}{7765} }

                                        =  <u>0.00397</u>

You might be interested in
Marcus was asked to find out what affects the strength of electromagnets. He was given a simple electromagnet made from a coil o
Alja [10]

Answer:

bncjk make sure bgfdf hi olb f see him be see vg hhzch

5 0
2 years ago
Consider the table of the powers of 8.
garri49 [273]
C loser that’s the correct number
8 0
2 years ago
PLEASE HELP!!!! 25 POINTS!!!!
Andrei [34K]

Answer:

0.9562

Step-by-step explanation:

Binomial probability is mathematically expressed as:

P(X=x)={n\choose x}p^x(1-p)^{n-x}

Given that p=0.18, n=5 ,  is calculated as:

P(X\leq 2)=P(0)+P(1)+P(2)\\\\={5\choose 0}0.18^0(1-0.18)^5+{5\choose 1}0.18^1(1-0.18)^4+{5\choose 2}0.18^2(1-0.18)^3\\\\=0.3707+0.4069+0.1786\\\\=0.9562

Hence, the probability of no more than 2 successes in 5 trials is 0.9562

4 0
3 years ago
Please help me answer this <br><br> Explain you’re answer <br><br> Will give braisnlt
lions [1.4K]
B the answer is B - hope this helps you out
7 0
3 years ago
Read 2 more answers
PLEASE HELP.find the solutions for a triangle with a =16 c =12 and b=63 degrees
givi [52]
A.16
b.12
c.63
try to have the triangle and draw a little drawling it will help
and start from there
7 0
3 years ago
Read 2 more answers
Other questions:
  • What is the data set
    5·1 answer
  • I need help with this problem <br><br><br><br> PLEASE HELP!
    12·1 answer
  • A map has a scale of 2 inches = 15 miles.If two towns are 7 inches apart on the map,how far apart are they actually
    14·2 answers
  • What is the area of the obtuse triangle below?
    5·1 answer
  • Express the first number as a percentage of the second number. 29 pounds of recyclable trash in a barrel of 53 pounds of trash.
    14·1 answer
  • 4•6*2 to the third power
    12·1 answer
  • I need to know the answers to 1-3
    7·1 answer
  • Answer if you want to be worshiped
    11·2 answers
  • What is the area of a circle with 22 diameter
    7·1 answer
  • (TUTORS WHERE R U?? KIDS NEED HELP LIKE ME!! ILL GIVE BRAINLYY)
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!