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
ki77a [65]
3 years ago
15

In a random sample of 75 American women age 18 to 30, 26 agreed with the statement that a woman should have the right to a legal

abortion for any reason (question wording: "Please tell me whether or not you think it should be possible for a pregnant woman to obtain a legal abortion if the woman wants it for any reason?"). In an independent random sample of 64 American women age 58 to 70, 21 agreed with the same statement. a) Test at the 1% significance level the hypothesis that the population proportions are equal, against the alternative that the population proportions are not equal. Include the p-value of your test statistic. b) Compute a 99% confidence interval for the difference of the two age group proportions. c) Are older women more or less likely than younger women to support abortion for any reason?
Mathematics
1 answer:
ddd [48]3 years ago
5 0

Answer:

a) z=\frac{0.347-0.328}{\sqrt{0.338(1-0.338)(\frac{1}{75}+\frac{1}{64})}}=0.236  

p_v =2*P(Z>0.236)=0.813  

If we compare the p value and using any significance level for example \alpha=0.01 always p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say that we don't have significant differences between the two proportions.  

b) We are confident at 99% that the difference between the two proportions is between -0.188 \leq p_B -p_A \leq 0.226

Step-by-step explanation:

Previous concepts and data given

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

p_A represent the real population proportion of women age 18 to 30  agreed with the statement that a woman should have the right to a legal abortion for any reason

\hat p_A =\frac{26}{75}=0.347 represent the estimated proportion of women age 18 to 30  agreed with the statement that a woman should have the right to a legal abortion for any reason

n_A=75 is the sample size for A

p_B represent the real population proportion for women age 58 to 70  agreed with the statement that a woman should have the right to a legal abortion for any reason

\hat p_B =\frac{21}{64}=0.328 represent the estimated proportion of women age 58 to 70  agreed with the statement that a woman should have the right to a legal abortion for any reason

n_B=64 is the sample size required for B

z represent the critical value for the margin of error and for the statisitc

The population proportion have the following distribution  

p \sim N(p,\sqrt{\frac{p(1-p)}{n}})

Part a

We need to conduct a hypothesis in order to check if the proportion are equal, the system of hypothesis would be:  

Null hypothesis:p_{A} = p_{B}  

Alternative hypothesis:p_{A} \neq p_{B}  

We need to apply a z test to compare proportions, and the statistic is given by:  

z=\frac{p_{A}-p_{B}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{A}}+\frac{1}{n_{B}})}}   (1)

Where \hat p=\frac{X_{A}+X_{B}}{n_{A}+n_{B}}=\frac{26+21}{75+64}=0.338

Calculate the statistic

Replacing in formula (1) the values obtained we got this:  

z=\frac{0.347-0.328}{\sqrt{0.338(1-0.338)(\frac{1}{75}+\frac{1}{64})}}=0.236  

Statistical decision

Since is a two sided test the p value would be:  

p_v =2*P(Z>0.236)=0.813  

If we compare the p value and using any significance level for example \alpha=0.01 always p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say that we don't have significant differences between the two proportions.  

Part b  

The confidence interval for the difference of two proportions would be given by this formula  

(\hat p_A -\hat p_B) \pm z_{\alpha/2} \sqrt{\frac{\hat p_A(1-\hat p_A)}{n_A} +\frac{\hat p_B (1-\hat p_B)}{n_B}}  

For the 99% confidence interval the value of \alpha=1-0.99=0.01 and \alpha/2=0.005, with that value we can find the quantile required for the interval in the normal standard distribution.  

z_{\alpha/2}=2.58  

And replacing into the confidence interval formula we got:  

(0.347-0.328) - 2.58 \sqrt{\frac{0.347(1-0.347)}{75} +\frac{0.328(1-0.328)}{64}}=-0.188  

(0.347-0.328) + 2.58 \sqrt{\frac{0.347(1-0.347)}{75} +\frac{0.328(1-0.328)}{64}}=0.226  

And the 99% confidence interval for the difference of proportions would be given (-0.188;0.226).  

We are confident at 99% that the difference between the two proportions is between -0.188 \leq p_B -p_A \leq 0.226

You might be interested in
PLEASE HELP I AM STUCK!!!THESE ARE ALL MY POINTS!!!
Bond [772]

Answer:

come back when you have the number for the 32oz

Step-by-step explanation:

8 0
3 years ago
What is the constant of proportionality for the graph? The graph is attached
hichkok12 [17]
The answer is A. 0.5. 

When you go out 1 on the X-axis you go up 0.5 on the Y-axis, thus the ratio is 0.5.

This is not easy to see, but if you go out 10 on the X-axis, it is easy to see that the Y-axis is at 5. Again giving the ratio 5/10=0.5
5 0
3 years ago
Tonya has a 1-quart, a 2-quart, and a 3-quart bowl. A recipe asks for 16 ounces of milk. If Tonya is going to triple the recipe,
Shalnov [3]
The answer would be the three quart bowl.Since it is clearly stated at the problem that if she 'triples' the recipe.So meaning, she needs to multiply each by three.So 1 quart = 3 quarts2 quarts = 6 quarts3 quarts = 9 quarts
So the smallest now would be the three quarts bowl.
3 0
3 years ago
Will mark brainliest!
Otrada [13]

Answer:

it's the third option

domain: x\geq 7\\range: y\geq 9

7 0
3 years ago
Read 2 more answers
a flat-bottom reflecting pool has length 30 yards, width 10 yards, and depth 0.3 yard. Find th e surface area of the pool and th
Zigmanuir [339]
The surface area of the object above can be calculated by summing up all the areas of the surfaces. Therefore, we will have 5 surfaces with rectangles as the shape. The volume would be the product of the length, width and the depth. We calculate as follows:

SA = 2(depth)(length) + 2(depth)(width) + (width)(length)
SA = 324 yd^2

VOlume = 30x10x.3
Volume = 90 yd^3
3 0
3 years ago
Other questions:
  • Find lim ?x approaches 0 f(x+?x)-f(x)/?x where f(x) = 4x-3
    15·1 answer
  • A circle with radius 6 has a sector with a central angle of 48º.
    8·2 answers
  • I need 100 topics done on aleks can someone help me it's worth a grade I'll give u my number so I can give u the info pls any ta
    13·1 answer
  • Find the center, vertices, and foci for the ellipse 25x^2+64y^2=1600
    13·2 answers
  • If PQ = 5 and QR = 17 , find PR
    15·1 answer
  • Você é um comandante de uma espaçonave. Sua missão é chegar até Alfa Centauro em cinco anos. A distância do Sol até Alfa Centaur
    6·1 answer
  • Alan drives 20.4 miles in 17 minutes.He passes a sign which gives the speed limit as 60mph.By how much in mph did Alan exceed th
    13·1 answer
  • Please look at the picture and answer it.
    10·1 answer
  • What operation is this that’s all
    13·1 answer
  • What is the perimeter of triangle ABC? Round the answer to the nearest tenth, if necessary.
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!