Statistics (Check Work)

Can Someone help me with these 2 problems? I am certain I am solving them correctly, but for some reason the computer keeps marking my answers as incorrect.

Question 1:
Minnesota had the highest turnout rate of any state for the 2012 Presidential election. Political analysts wonder if turnout in rural Minnesota was higher than turnout in the urban areas of the state. A sample shows that 663 of 884 registered voters from rural Minnesota voted in the 2012 Presidential election, while 414 out of 575 registered voters from urban Minnesota voted.

-- At = .05, test the hypothesis. What is the p-value, and what conclusion do you to draw from your results?
-- My work: to get the P-value, I first computed the pooled estimate:
854(.75)+575(.72)/884+575= 0.7382
then i used that number in the equation for test statistic for hypothesis tests about p1-p2
(.75-.72)/√.7382(1-.7382)(1/884+1/575)=1.27
I get 1.27 as the z score and the value associated0 with that is .8980, which i subtracted from 1 to get the area in the upper tale and i got .102 which i thought you would multiply by 2 to get the P-value, however, the computer is marking .204 as incorrect.

Question 2:
Adecco Workplace Insights Survey sampled men and women workers and asked if they expected to get a raise or promotion this year. Suppose the survey sampled 200 men and 200 women. If 104 of the men replied yes and 74 of the women replied yes, are the results statistically significant in that you can conclude a greater proportion of men are expecting to get a raise or a promotion this year?

--Use a .01 level of significance. What is the p-value? Round your answer to four decimal places.
--My work:I followed the exact same procedure as above, however, the P-value that I got of .0026 is inncorrect according to the computer.

Can someone please help me? I always seem to struggle with the P-value. Thank you so much in advance.

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asked by Jen
  1. Is it possible for " MathGuru " to help with this question? Last time he provided a very detailed explanation. It really helped me understand the concepts.

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    posted by Jen
  2. I played around with some of the answers, and I realized my mistake. Turns out the computer just wanted me to compute the right tailed P-value.

    First Question:
    1-0.8980=0.1020

    Second Question:
    1-9987=0.0013

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    posted by Jen
  3. Hi Jen! Just an FYI: I'm a "she" instead of a "he" but thanks for the compliments. I'm always glad to help when and where I can.

    Let's get started. Both questions are the same type of problem.

    Question 1:

    Null: pR = pU
    Alternate: pR > pU

    Formula:
    z = (pR - pU)/√[pq(1/n1 + 1/n2)]

    Note: R = rural; U = urban
    p = (x1 + x2)/(n1 + n2) = (663 + 414)/(884 + 575) = 1077/1459 = .7382
    q = 1 - p = .2618
    pR = 663/884 = .75
    pU = 414/575 = .72

    Now we plug in the numbers:
    z = (.75 - .72)/√(.7382)(.2618)(1/884 + 1/575) = .03/√(.1933)(.00113 + .00174) = .03/√(.1933)(.00287) = .03/√.000554771 = .03/.02355 = 1.27

    I get .102 as well for the p-value. The p-value would be the area to the right of the test statistic for the one-tailed alternate hypothesis using "greater than" in its statement. (If you have a two-tailed test, you multiply your answer by 2.)

    Question 2:

    This is also a one-tailed test using "greater than" in its alternate hypothesis statement.

    z = (104/200 - 74/200)/√[pq(1/200 + 1/200)
    p = (104 + 74)/(200 + 200) = 178/400 = .445
    q = 1 - p = .555
    z = (.52 - .37)/√(.445)(.555)(.005 + .005) = .15/.049696579 = 3.018

    p-value is .0013 -->p-value would be the area to the right of the test statistic.

    I hope this helps.

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  4. I see you figured this out on your own. Good job!

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  5. I am so sorry! My apologizes for assuming you were a male! You have really been a great help on the few questions I have posted on here. I appreciate it so much!

    I did figure it out. I was going by the notes from my textbook, and they kept multiplying the p-value by 2 on every example, so I assumed I needed to as well.

    Thank you for the clarification again! It means so much.

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    posted by Jen
  6. Looks like you have a good handle on this, Jen. Keep up the good work!

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  7. What is the sample proportion for the men in question 2 and the proportion for women?

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    posted by Kim

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