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
sesenic [268]
3 years ago
13

A simple random sample (SRS) of 100 of a certain popular car in 1997 found that 20 had a certain minor defect in the brakes. An

SRS of 400 of the same car in 1998 found that 50 had the minor defect in the brakes. Let p1 and p2 be the proportion of all cars of this model in 1997 and 1998, respectively,that contained the defect. A 90% confidence interval for p1−p2 is:
Mathematics
1 answer:
densk [106]3 years ago
5 0

Answer: The required interval is (0.679, 0.821).

Step-by-step explanation:

Since we have given that

n_1=100\\\\p_1=20\\\\n_2=400\\\\p_2=50

So, the proportions would be

\hat{p_1}=\dfrac{p_1}{n_1}=\dfrac{20}{100}=0.2\\\\\hat{p_2}=\dfrac{p_2}{n_2}=\dfrac{50}{400}=0.125

So, At 90% confidence interval, the z score value would be

z = 1.65

and the hypothesis are :

H_0:\hat{p_1}-\hat{p_2}=0\\\\H_1:\hat{p_1}-\hat{p_2}\neq 0

So, the 90% confidence interval would be

(\hat{p_1}-\hat{p_2})\pm z\sqrt{\dfrac{\hat{p_1}(1-\hat{p_1}}{n_1}+\dfrac{\hat{p_2}(1-\hat{p_2})}{n_2}}\\\\=(0.2-0.125)\pm 1.65\sqrt{\dfrac{0.2\times 0.8}{100}+\dfrac{0.125\times 0.875}{400}}\\\\=0.075\pm 1.65\times 0.0433\\\\=(0.75-0.0714,0.75+0.0714)\\\\=(0.679,0.821)

Hence, the required interval is (0.679, 0.821).

You might be interested in
Simplify x^2-4x+4/x^2-4
MatroZZZ [7]

Answer:

x2 - 4x - 4

 ———————————

    x - 2  

Step-by-step explanation:

4 0
3 years ago
Find 51* 49 USING MENTAL MATH'
Nesterboy [21]
I used mental math and it took a long time, but I got the answer of 2,499.
7 0
3 years ago
Read 2 more answers
Help meee please <br><img src="https://tex.z-dn.net/?f=%20%20%5Csqrt%7B%3F%7D%20%7B78%7D%20%7D%20" id="TexFormula1" title=" \sq
tekilochka [14]
I think it is 8.83? I am not positive but it is worth a try
7 0
2 years ago
Korey’s comic book store has been up and running for 4 years. Korey feels that his store has been successful and is considering
Inessa05 [86]
Year      Net Profit
1            <span>$14,250.00
2            $15,390.00
3            $16,621.20
4            $17,950.90</span>2

We need to get the increase of the net profit of the current year from the previous year.

Percentage increase = (Current year - Previous Year)/ Previous Year    * 100%

Year 2:  (15,390 - 14, 250) / 14,250   * 100% = 0.08 * 100% = 8%
Year 3: (16,621.20 - 15,390) / 15,390 * 100% = 0.08 * 100% = 8%
Year 4: (17,950.90 - 16,621.20) / 16,621.20 * 100% = 0.08 * 100% = 8%

Every year the net income increases by 8%. So, the net income in Year 5 will be:

17,950.90 x 1.08 = 19,386.97  Choice D.

8 0
3 years ago
Read 2 more answers
What does 1 ft equal to​
Katyanochek1 [597]
Equal in what? Cm, m, mm ?
6 0
3 years ago
Read 2 more answers
Other questions:
  • Last one lol I promise
    7·1 answer
  • A basketball weighs an average of 22 ounces, and it is possible for its weight to vary at most 0.75 ounces from this average. Wh
    9·1 answer
  • When seven times a number is deceased by 3, the result is 25. What is the number?
    8·2 answers
  • Please help my brain hurts so bad I can’t even see straight tbh
    11·1 answer
  • What is 309,017 in expanded form
    8·2 answers
  • 80.3 time 0.58 must show work
    12·1 answer
  • HELP PICTURE IS SHOWN
    10·2 answers
  • emma wants a barbie doll that cost $7.00 . she had only $3.29. how many more money she needs to buy a barbie? use estimate to so
    13·1 answer
  • Recovery
    10·1 answer
  • Consider the line y = 7x-5.
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!