Mathematics, 18.12.2019 03:31 bellabae8390

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: " 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?

Answers: 2

Show answers

Answers

Answer from: Dweath50

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(Z0.236)=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

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(Z0.236)=0.813

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 $-0.188 \leq p_B -p_A \leq 0.226$

Answer from: Quest

The decimal expansion would be .27 repeated

Answer from: Quest

the answer is d

step-by-step explanation:

Another question on Mathematics

Mathematics, 21.06.2019 18:30

This is my question~~ ( r ^ 4 - 2r ^ 3 - 23 r ^ 2 - 4r - 32)÷(r+4) ~~ i must use long division to solve it : / i was wondering if anyone world like to solve it. and if so, share step-by-step explanations! you! ❤

Answers: 2

Answer

Mathematics, 21.06.2019 20:00

Cody started biking to the park traveling 15 mph, after some time the bike got a flat so cody walked the rest of the way, traveling 4 mph. if the total trip to the park took 6 hours and it was 46 miles away, how long did cody travel at each speed? solve using rate times time= distance

Answers: 1

Answer

Mathematics, 21.06.2019 20:30

Find the magnitude, correct to two decimal places, made by each of the following with positive direction of the x axis a) y= x the answer is 45° but i don’t know how

Answers: 2

Answer

Mathematics, 21.06.2019 23:00

How many 2/5s are in 1 and 1/2 plz someone me right now

Answers: 1

Answer

You know the right answer?

In a random sample of 75 american women age 18 to 30, 26 agreed with the statement that a woman shou...

Questions

Mathematics, 13.10.2020 01:01

A parallelogram has vertices A(-2,1), B(3,2), C(4,6), D(-1,5). At what point do the diagonals intersect? PLZZ HEL A. (1,3 1/2) B. (2,3 1/2)