Explore BrainMass

Explore BrainMass

    Inferences: One population

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    A portion of the data file for the hospital that collected the data on hand washing is shown below:

    Observation Unit Time 1 Time 2
    1 CCU 3 16
    2 CCU 2 7
    3 CCU 0 5
    4 CCU 5 8
    5 CCU 2 15
    6 CCU 0 15
    7 CCU 2 20
    8 CCU 3 16
    9 CCU 0 18
    10 IMCU 1 16
    11 IMCU 2 8

    You can see that information was also collected on the unit of the employee and a second time, labeled Time 2, was also recorded. Assume that the hand-washing times are normally distributed and are recorded in seconds.

    a). Find the sample means and sample standard deviations for the first hand-washing time, Time 1, for each unit.
    b). Test to see if any of the units had an average hand-washing time, Time 1, less than 5 seconds.
    c). The second hand-washing time, Time 2 was recorded after the employees received some training on the effects of not washing their hands long enough. Find the sample means and sample standard deviations for the second hand-washing time, Time 2, for each unit.
    d). Test to see if any of the units had an average hand-washing time after training, Time 2, of less than 5 seconds.
    e). Display all the initial hand-washing times, Time 1 in a histogram. Is the assumption of normality reasonable?
    f). Display all the second hand-washing times, Time 2, in a histogram. Is the assumption of normality reasonable?
    g). Test the hypothesis that the variance of the initial hand-washing time is 14 seconds.
    h). Test the hypothesis that the variance of the hand-washing times after training is greater than 14 seconds.
    i). Find the sample proportion of employees who increased their hand-washing time after training. Test the hypothesis that the proportion of employees who increased their time after training is greater than 0.80.
    j). Based on your analysis, write a short report to the manager of the hospital.

    © BrainMass Inc. brainmass.com March 4, 2021, 5:46 pm ad1c9bdddf
    https://brainmass.com/statistics/chi-squared-test/inferences-one-population-9929

    Solution Preview

    a.)
    For CCU (say x):
    sum(x) = 17
    n = 9
    mean = <x> = 17/9 = 1.89 --Answer
    Variance:
    => Var(x) = sum((x-<x>)^2)/(n-1)
    => Var(x) = (sum(x^2) - n*<x>^2)/(n-1) = (55 - 9*(17/9)^2)/8 = 2.86
    => SD = sqrt(Variance) = sqrt(2.86) = 1.69 --Answer

    FOR IMCU (say y):
    sum(y) = 3
    <y> = 3/2 = 1.5 --Answer
    Variance = ((1-1.5)^2 + (2-1.5)^2)/(2-1) = (0.25+0.25)/1 = 0.5
    => SD = sqrt(variance) = sqrt(0.5) = 0.707 --Answer

    b.)
    with 95% confidence level: alpha = 0.05: alpha/2 = 0.025
    For CCU:
    mu = <x> +or- t(0.025)*SD/sqrt(9)
    t(0.025) for d.f. 8 = 2.306
    => mu = 1.89 +or- 2.306*1.69/sqrt(9) = (3.189,0.591)

    FOR IMCU:
    t(0.025) for d.f. 1 = 12.706
    mu = 1.5 +or- 12.706*0.707/sqrt(2) = (7.85, -4.85)
    Units CCU has average hand-washing times less than 5 second but, IMCU can have greater than 5 sec. ...

    Solution Summary

    The solution answers the question(s) below.

    $2.49

    ADVERTISEMENT