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
Factoring the expression 15x+6 using GCF
s344n2d4d5 [400]
The answer is 3(5x+2) i hope this helps you.
3 0
3 years ago
Find the slope of the line that passes through (40,3000) and (60, 4000).
iragen [17]

Answer:

m=50

General Formulas and Concepts:

<u>Pre-Alg</u>

  • Order of Operations: BPEMDAS

<u>Algebra I</u>

  • Slope Formula: m=\frac{y_2-y_1}{x_2-x_1}

Step-by-step explanation:

<u>Step 1: Define</u>

Point (40, 3000)

Point (60, 4000)

<u>Step 2: Find slope </u><em><u>m</u></em>

  1. Substitute:                    m=\frac{4000-3000}{60-40}
  2. Subtract:                       m=\frac{1000}{20}
  3. Divide:                          m=50
3 0
3 years ago
Find four consecutive multiples of<br> 5 with a sum of 210.
olganol [36]
It’s 42 heheeeee I’m Michel Jackson
7 0
3 years ago
Read 2 more answers
6) If the perimeter of the equilateral triangle ABC is x inches. The mid points of the sides are joined to form the smaller tria
Nataliya [291]

Answer:

96 in

Step-by-step explanation:

If the midpoints of the sides are joined to form the smaller triangle, then the perimeter of the smaller triangle is half the perimeter of the greater triangle, because the sides of the smaller triangle are midlines of the greater triangle. By the triangle's midline theorem, each triangle's midline is half the side to which this midline is parallel.

So, if the perimeter of 6th triangle is 3 inches, then the perimeter of 5th triangle is 6 inches, the perimeter of 4th triangle is 12 inches, the perimeter of 3rd triangle is 24 in, the perimeter of 2nd triangle is 48 in and the perimeter of the initial triangle is 96 in

6 0
3 years ago
I just got back from winter break for my school and I already forgot everything INCLUDING the seriously easy things ;)
Natasha_Volkova [10]

Answer:

112cm

Step-by-step explanation:

4×2=8

8×2=16

4×8=32

8+16+32= 56×2= 112cm

Hope this helps!

7 0
3 years ago
Read 2 more answers
Other questions:
  • Which inequality statement is true?
    6·1 answer
  • Any Help Please?!
    7·1 answer
  • Need help with number 3 &amp; 5 please .
    8·1 answer
  • Asha and Lucy are selling pencils in a school shop.
    9·1 answer
  • Find the measurement?
    6·1 answer
  • Which relation is a function?
    7·1 answer
  • A rectangular field has a length of x metres.
    14·1 answer
  • Pls answer. im not smart
    7·1 answer
  • Help me pls pls pls
    11·1 answer
  • What is 27 written as exponential notation?
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!