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
Cerrena [4.2K]
3 years ago
7

The National Vital Statistics Reports for November 2011 states that U.S. preterm birth rate for 2010 was about 12%. Preterm birt

h means premature birth. Suppose that this year a random sample of 500 births has 52 that are preterm. Prompt Using the estimate from the NVS Report for 2011 and the result from this year’s random sample, estimate the percent of preterm births this year with 95% confidence interval. (Be sure to check that a normal model is appropriate and show your work for calculating the 95% confidence in a fashion similar to the examples.)
Mathematics
2 answers:
miskamm [114]3 years ago
6 0

Answer:

0.104 - 1.96\sqrt{\frac{0.104(1-0.104)}{500}}=0.0772

0.104 + 1.96\sqrt{\frac{0.104(1-0.104)}{500}}=0.1308

The 95% confidence interval would be given by (0.0772;0.1308)

Step-by-step explanation:

For this case we can calculate the estimated proportion like this:

\hat p =\frac{52}{500}= 0.104

We can assume that the normal model can be used since we satisfy two conditions:

np =500*0.104= 52>10

n(1-p) = 500*(1-0.104) = 448>10

The confidence level for this case is 95% of confidence, and the significance is given by \alpha=1-0.95=0.05 and \alpha/2 =0.025. And the critical value would be given by:

z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96

The confidence interval for the mean is given by the following formula:  

\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}

Replacing the values we got:

0.104 - 1.96\sqrt{\frac{0.104(1-0.104)}{500}}=0.0772

0.104 + 1.96\sqrt{\frac{0.104(1-0.104)}{500}}=0.1308

The 95% confidence interval would be given by (0.0772;0.1308)

Brilliant_brown [7]3 years ago
3 0

Answer:

Therefore, the 95% confidence interval would be given by= (0.0771 , 0.1309)

Step-by-step explanation:

Given : Sample size=n=500

Let, X be the number of preterm.

Here , X=52

The sample proportion is , p=X/n=52/500=0.1040

q= 1 - p = 0.8960

Therefore , the 95% confidence interval estimate for the percent of preterm of births this year is ,

P\pm Z_{\alpha /2}\sqrt{\frac{pq}{n} }

0.1040 \pm Z_{0.05/2}\sqrt{\frac{0.1040 \times 0.8960}{500} } \\\\0.1040*1.96*0.0137

From normal probability integral table;

Z_{0.05/2} =1.96\\\\0.1040 \pm 0.0269

Therefore, the 95% confidence interval would be given by= (0.0771 , 0.1309)

You might be interested in
The logo for a new company is a circle divided into 24 equally sized sectors. Six of the sectors are white, and the others are d
AveGali [126]

Answer:

r = 2.5

Step-by-step explanation:

the area of the whole circle = \frac{13}{50}*π * 24

A = πr² = (13π*24)/50

r = √((13*24)/50) = 2.5 inches

8 0
3 years ago
7 - 3b-2(0 + 3 - 2b)
Naddika [18.5K]

Step-by-step explanation:

7 - 3b-2(0 + 3 - 2b)

To simplify the expression in the box, Fatua used

these steps:

Step 1:7 - 3b-2(3 - 3b)

Step 2:7 - 3-6-36-

Step 3: -13 - 66

Did Fatua calculate correctly? if nnot, in what step

did she make her FIRST mistake?

6 0
2 years ago
Read 2 more answers
X - 3/8 = 3/6 <br><br> what is x.
Anna71 [15]
X-3/8=3/6
Add 3/8 to both sides, to leave the variable alone
X= 3/6-3/8
Use common denominators-8 (3/6 is 1/2)
X= 4/8-3/8
X=1/8
7 0
3 years ago
Read 2 more answers
If the real exchange rate is 5/4 pounds of Chilean beef per pound of U.S. beef, a pound of U.S. beef costs $2 and the nominal ex
bearhunter [10]
I do u u look de las mejores canciones
5 0
2 years ago
Which algebraic expression has like terms?
Mariana [72]

Answer:

The answer is c I think

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Other questions:
  • Find the first, fourth, and eighth terms of the sequence. A(n) = –3 • 2^n–1
    15·1 answer
  • Five computer program modules are ranked as M1, M2, M3, M4, and M5 according to the ascending order of effort required to debug
    15·1 answer
  • The perimeter of rectangle ABCD is 42 cm and the area is 80 cm2. Which equation can be used to find the dimensions of the rectan
    10·1 answer
  • The phone company charges a flat rate of $25 per month. In addition they charge $0.05 for each minute of service Which equation
    10·1 answer
  • Mr Patel is planning to drive 325 miles. He will stop one hour for lunch and take a 15 min rest break.
    10·1 answer
  • Please solve, I have more of these to solve
    14·1 answer
  • The sum of the measures of the interior angles of a polygon with n sides is __.
    5·2 answers
  • NEED HELP ASAP PLEASE
    9·1 answer
  • Donna finished 67% of her homework. What fraction of her homework is completed?
    9·1 answer
  • 1. What would be the depth of water of 3/4 filled rectangular pool, if pool is 10 m long, 7 m wide and 8 m deep?
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!