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
gulaghasi [49]
3 years ago
9

A certain geneticist is interested in the proportion of males and females in the population who have a minor blood disorder. In

a random sample of 1000 males, 250 are found to be afflicted, whereas 275 of 1000 females tested appear to have the disorder. Compute a 95% confidence interval for the difference between the proportions of males and females who have the blood disorder.
Mathematics
1 answer:
lord [1]3 years ago
8 0

Answer:

95% confidence interval for the difference between the proportions of males and females who have the blood disorder is [-0.064 , 0.014].

Step-by-step explanation:

We are given that a certain geneticist is interested in the proportion of males and females in the population who have a minor blood disorder.

A random sample of 1000 males, 250 are found to be afflicted, whereas 275 of 1000 females tested appear to have the disorder.

Firstly, the pivotal quantity for 95% confidence interval for the difference between population proportion is given by;

                        P.Q. = \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 males having blood disorder= \frac{250}{1000} = 0.25

\hat p_2 = sample proportion of females having blood disorder = \frac{275}{1000} = 0.275

n_1 = sample of males = 1000

n_2 = sample of females = 1000

p_1 = population proportion of males having blood disorder

p_2 = population proportion of females having blood disorder

<em>Here for constructing 95% confidence interval we have used Two-sample z proportion statistics.</em>

<u>So, 95% confidence interval for the difference between the population proportions, </u><u>(</u>p_1-p_2<u>)</u><u> is ;</u>

P(-1.96 < N(0,1) < 1.96) = 0.95  {As the critical value of z at 2.5% level

                                             of significance are -1.96 & 1.96}  

P(-1.96 < \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}} } < 1.96) = 0.95

P( -1.96 \times {\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+ \frac{\hat p_2(1-\hat p_2)}{n_2}} } < {(\hat p_1-\hat p_2)-(p_1-p_2)} < 1.96 \times {\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+ \frac{\hat p_2(1-\hat p_2)}{n_2}} } ) = 0.95

P( (\hat p_1-\hat p_2)-1.96 \times {\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+ \frac{\hat p_2(1-\hat p_2)}{n_2}} } < (p_1-p_2) < (\hat p_1-\hat p_2)+1.96 \times {\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+ \frac{\hat p_2(1-\hat p_2)}{n_2}} } ) = 0.95

<u>95% confidence interval for</u> (p_1-p_2) =

[(\hat p_1-\hat p_2)-1.96 \times {\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+ \frac{\hat p_2(1-\hat p_2)}{n_2}} }, (\hat p_1-\hat p_2)+1.96 \times {\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+ \frac{\hat p_2(1-\hat p_2)}{n_2}} }]

= [ (0.25-0.275)-1.96 \times {\sqrt{\frac{0.25(1-0.25)}{1000}+ \frac{0.275(1-0.275)}{1000}} }, (0.25-0.275)+1.96 \times {\sqrt{\frac{0.25(1-0.25)}{1000}+ \frac{0.275(1-0.275)}{1000}} } ]

 = [-0.064 , 0.014]

Therefore, 95% confidence interval for the difference between the proportions of males and females who have the blood disorder is [-0.064 , 0.014].

You might be interested in
If the cow can't ran over the car?
adell [148]
Lol what I don't understand what u are asking
8 0
3 years ago
Multiply: <br> <img src="https://tex.z-dn.net/?f=%5Cfrac%7B8n%5E%7B2%7D%20%7D%7Bm%5E%7B2%7D-16%20%7D" id="TexFormula1" title="\f
Mkey [24]

9514 1404 393

Answer:

  4mn/(3m+12)

Step-by-step explanation:

It is often helpful to factor expressions so that common factors can cancel.

  \dfrac{8n^2}{m^2-16}\times\dfrac{m^2-4m}{6n}=\dfrac{8mn^2(m-4)}{6n(m-4)(m+4)}=\dfrac{4mn}{3(m+4)}\\\\=\boxed{\dfrac{4mn}{3m+12}}

3 0
2 years ago
FIND THE VALUE OF LOG 16 BASE 1/2
Molodets [167]
The result can be shown in both exact and decimal forms.Exact Form:<span><span>−<span>14</span></span><span>-<span>14</span></span></span>Decimal Form:<span>−<span>0.25




</span></span>
3 0
3 years ago
Can someone please help me with this?
valentina_108 [34]

Answer:

L: 110 W: 90

Step-by-step explanation:

110 + 110 + 90 + 90=400 (perimeter)

110 x 90 =9900 (new area that is greater than the original)

ding ding.

also this was not worth only five pts man LOL

3 0
2 years ago
Read 2 more answers
A park creates new habitats for 182 monkeys. Each habitat will house 8 or fewer monkeys. What did you do with the remainder? exp
Anuta_ua [19.1K]
32 because 1plus 31 equals 32
7 0
3 years ago
Read 2 more answers
Other questions:
  • Given the following computer printout for a set of sample data, which one of the following represents the value of the Interquar
    10·1 answer
  • 1. Round to the nearest hundred, and then subtract 4,623-3,892
    12·1 answer
  • Zachary purchased a computer for 1800 on a payment plan. Three months after he purchased the computer, his balance was 1350. Fiv
    5·2 answers
  • What is 2,443,802,280 rounded to the nearest ten millon
    7·2 answers
  • 5. A soccer ball is kicked from the ground level with an upward velocity of 60 feet per second. The
    14·1 answer
  • Please answer fast!!!!!!!!!!!
    5·1 answer
  • Point C is on the midpoint of a section of highway, represented by AB. If AB = 32 miles,
    7·1 answer
  • What is the probability that you will be able to draw all of the cards in the deck without being forced to stop because you have
    15·1 answer
  • A cylinder has a height of 8 inches and a radius of 11 inches. What is its volume? round your answer to the nearest hundredth.
    14·1 answer
  • In , side is extended to point E. When connected to vertex A, segment is parallel to segment . In this construction, you are giv
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!