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Math Help - statisics and probabillity North American Quiz

  1. #1
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    statisics and probabillity North American Quiz

    Hi, I just wrote a North American knowlege quiz for statistics and probabillity.
    These were the questions. Can someone solve any of these and show your work? I just need to check if i did it correctly... nervous....


    Long Answer Questions

    3. In an investigation of pregnancy-induced hypertension, one group of women with this
    disorder was treated with low-dose aspirin, and a second group was given a placebo. A
    sample consisting of 23 women who received aspirin has mean arterial blood pressure
    111 mm Hg and standard deviation 8 mm Hg; a sample of 24 women who were given
    the placebo has mean blood pressure 109 mm Hg and standard deviation 8 mm Hg.
    a. [5] At the 0.01 level of signi cance, test the null hypothesis that the two populations
    of women have the same mean arterial blood pressure.
    b. [4] Construct a 99% con dence interval for the true di erence in population means.
    Does this interval contain the value 0?


    4. [8] Online ads targeting children were said to have decreased at least 56% between
    May and August 2000. A sample of 100 ads selected during this period showed a 45%
    decrease in online ads targeting children. State the null and alternative hypotheses
    and carry out the test at the 1% level of signi cance.


    5. A fast food franchiser is considering building a restaurant at a certain location. Ac-
    cording to a nancial analysis, a site is acceptable only if the number of pedestrians
    passing the location averages more than 100 per hour. A random sample of 50 hours
    produced x = 110 and s = 12 pedestrians per hour.
    a. [5] Do these data provide sucient evidence to establish that the site is acceptable?
    Use = 0:05.
    b. [3] What are the consequences of Type I and Type II errors? Which error is more
    expensive to make?
    c. [2] Considering your answer in part (b), should you select to be large or small?
    Explain.
    d. [3] What assumptions about the number of pedestrians passing the location in an
    hour are necessary for your hypothesis test to be valid?


    6. [10] A company is interested in o ering its employees one of two employee bene t
    packages. A random sample of the company's employees is collected, and each person
    in the sample is asked to rate each of the two packages on an overall preference scale
    of 0 to 100. Results were
    Program A: 45, 67, 63, 59, 77, 69, 45, 39, 52, 58, 70
    Program B: 56, 70, 60, 45, 85, 79, 50, 46, 50, 60, 82
    Do you believe that the employees of this company prefer, on the average, one package
    over the other? Explain.


    7. [10] Data from the Bureau of Labor Statistics indicate that in one recent year the
    unemployment rate in Cleveland was 7.5% and unemployment rate in Chicago was
    7.2%. Suppose that both gures are based on random samples of 1,000 people in each
    city. Test the null hypothesis that the unemployment rates in both cities are equal
    versus the alternative hypothesis that they are not equal. What is the p-value? State
    your conclusion.
    2


    8. A chemical manufacturer claims that the purity of his product never varies by more
    than 2%. Five batches were tested and given purity reading of 98.2, 97.1, 98.9, 97.7,
    and 97.9%.
    a. [4] Do the data provide sucient evidence to contradict the manufacturer's claim?
    (To be generous, let a range of 2% equal 4.)
    b. [4] Find a 90% con dence interval for 2.
    c. [2] Under which conditions, the con dence interval and test hypothesis in part (a)
    and (b) are valid?


    9. The following data were obtained in an experiment relating the dependent variable, y
    (texture of strawberries) , with x (coded storage temperature).
    x -2 -2 0 2 2
    y 4.0 3.5 2.0 0.5 0.0
    a. [4] Calculate the correlation coecient between x and y.
    b. [6] What is the regression line for predicting texture of strawberries based on coded
    storage temperature.
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  2. #2
    Bar0n janvdl's Avatar
    Joined
    Apr 2007
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    South Africa
    Posts
    1,630
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    Quote Originally Posted by andrea4unu View Post
    Hi, I just wrote a North American knowlege quiz for statistics and probabillity.
    These were the questions. Can someone solve any of these and show your work? I just need to check if i did it correctly... nervous....


    Long Answer Questions

    3. In an investigation of pregnancy-induced hypertension, one group of women with this
    disorder was treated with low-dose aspirin, and a second group was given a placebo. A
    sample consisting of 23 women who received aspirin has mean arterial blood pressure
    111 mm Hg and standard deviation 8 mm Hg; a sample of 24 women who were given
    the placebo has mean blood pressure 109 mm Hg and standard deviation 8 mm Hg.
    a. [5] At the 0.01 level of signicance, test the null hypothesis that the two populations
    of women have the same mean arterial blood pressure.
    b. [4] Construct a 99% condence interval for the true dierence in population means.
    Does this interval contain the value 0?


    4. [8] Online ads targeting children were said to have decreased at least 56% between
    May and August 2000. A sample of 100 ads selected during this period showed a 45%
    decrease in online ads targeting children. State the null and alternative hypotheses
    and carry out the test at the 1% level of signicance.


    5. A fast food franchiser is considering building a restaurant at a certain location. Ac-
    cording to a nancial analysis, a site is acceptable only if the number of pedestrians
    passing the location averages more than 100 per hour. A random sample of 50 hours
    produced x = 110 and s = 12 pedestrians per hour.
    a. [5] Do these data provide sucient evidence to establish that the site is acceptable?
    Use = 0:05.
    b. [3] What are the consequences of Type I and Type II errors? Which error is more
    expensive to make?
    c. [2] Considering your answer in part (b), should you select to be large or small?
    Explain.
    d. [3] What assumptions about the number of pedestrians passing the location in an
    hour are necessary for your hypothesis test to be valid?


    6. [10] A company is interested in oering its employees one of two employee benet
    packages. A random sample of the company's employees is collected, and each person
    in the sample is asked to rate each of the two packages on an overall preference scale
    of 0 to 100. Results were
    Program A: 45, 67, 63, 59, 77, 69, 45, 39, 52, 58, 70
    Program B: 56, 70, 60, 45, 85, 79, 50, 46, 50, 60, 82
    Do you believe that the employees of this company prefer, on the average, one package
    over the other? Explain.


    7. [10] Data from the Bureau of Labor Statistics indicate that in one recent year the
    unemployment rate in Cleveland was 7.5% and unemployment rate in Chicago was
    7.2%. Suppose that both gures are based on random samples of 1,000 people in each
    city. Test the null hypothesis that the unemployment rates in both cities are equal
    versus the alternative hypothesis that they are not equal. What is the p-value? State
    your conclusion.
    2


    8. A chemical manufacturer claims that the purity of his product never varies by more
    than 2%. Five batches were tested and given purity reading of 98.2, 97.1, 98.9, 97.7,
    and 97.9%.
    a. [4] Do the data provide sucient evidence to contradict the manufacturer's claim?
    (To be generous, let a range of 2% equal 4.)
    b. [4] Find a 90% condence interval for 2.
    c. [2] Under which conditions, the condence interval and test hypothesis in part (a)
    and (b) are valid?


    9. The following data were obtained in an experiment relating the dependent variable, y
    (texture of strawberries) , with x (coded storage temperature).
    x -2 -2 0 2 2
    y 4.0 3.5 2.0 0.5 0.0
    a. [4] Calculate the correlation coecient between x and y.
    b. [6] What is the regression line for predicting texture of strawberries based on coded
    storage temperature.
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