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    Bar Charts and Confidence Interval

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

    The following data were collected on the examination results of biology students in 4 second level biology modules: There were 20 - 30 students in each class:

    1. Vertebrate Physiology & Evolution:
    56, 57, 67, 75, 45, 35, 56, 67, 82, 91, 58, 60, 61, 63, 76, 54, 36, 45, 67, 57, 60, 63, 76, 78, 50, 60, 54.

    2. Practical Skills for Scientists
    74, 67, 84, 67, 54, 89, 92, 95, 54, 67, 78, 78, 67, 73, 77, 80, 81, 85, 94, 87, 86

    3. Cells & Sugars
    56, 45, 34, 23, 45, 56, 67, 35, 45, 30, 28, 28, 35, 38, 42, 44, 58, 45, 34, 45, 57, 56, 32.

    4. Introductory Microbiology
    45, 67, 57, 55, 56, 59, 57, 59, 60, 64, 62, 63, 64, 64, 65, 63, 56, 58, 52, 53, 64, 65, 64, 53, 58, 55, 54, 62, 58, 60.

    Plot these data with their associated confidence limits on a bar chart and write a paragraph what the data indicates.

    © BrainMass Inc. brainmass.com December 24, 2021, 9:16 pm ad1c9bdddf
    https://brainmass.com/statistics/statistical-figures/bar-charts-confidence-interval-361352

    SOLUTION This solution is FREE courtesy of BrainMass!

    The 95% confidence interval for the mean score in Vertebrate Physiology and Evolution is given as:
    (x ̅-(z_(α/2) s)/√n,x ̅+(z_(α/2) s)/√n)

    where,Sample Size,n=27
    Mean,x ̅=61.074
    Standard Deviation,s=13.182

    z_(α/2) for 95% confidence=1.96
    Thus the 95% confidence interval for the mean score is given as

    (61.074-(1.96×13.182)/√27,61.074+(1.96×13.182)/√27)

    =(61.074-4.972,61.074+4.972)

    =(56.102,66.046)

    The 95% confidence interval for the mean score in Practical Skills for Scientists is given as:
    (x ̅-(z_(α/2) s)/√n,x ̅+(z_(α/2) s)/√n)

    where,Sample Size,n=21
    Mean,x ̅=77.571
    Standard Deviation,s=11.788

    z_(α/2) for 95% confidence=1.96
    Thus the 95% confidence interval for the mean score is given as

    (77.571-(1.96×11.788)/√21,77.571+(1.96×11.788)/√21)

    =(77.571-0.765,77.571+0.765)

    =(76.806,78.336)

    The 95% confidence interval for the mean score in Cells & Sugars is given as:
    (x ̅-(z_(α/2) s)/√n,x ̅+(z_(α/2) s)/√n)

    where,Sample Size,n=23
    Mean,x ̅=42.522
    Standard Deviation,s=13.182

    z_(α/2) for 95% confidence=1.96
    Thus the 95% confidence interval for the mean score is given as

    (42.522-(1.96×11.630)/√23,42.522+(1.96×11.630)/√23)

    =(42.522-4.753,42.522+4.753)

    =(37.769,47.275)

    The 95% confidence interval for the mean score in Introductory Microbiology is given as:
    (x ̅-(z_(α/2) s)/√n,x ̅+(z_(α/2) s)/√n)

    where,Sample Size,n=30
    Mean,x ̅=59.067
    Standard Deviation,s=4.968

    z_(α/2) for 95% confidence=1.96
    Thus the 95% confidence interval for the mean score is given as

    (59.067-(1.96×4.968)/√30,59.067+(1.96×4.968)/√30)

    =(59.067-4.972,59.067+4.972)

    =(54.095,64.039)

    Please refer to the EXCEL sheet for the Bar Charts.
    The given data indicates the scores on the respective modules. The average scores on each module are given by their mean values. The variance and standard deviation indicates how much the scores in each subject vary from their respective means. The greater the value of the variance or standard deviation, the higher is the amount by which the scores vary from their respective means. The scores in Vertebrate Physiology & Evolution show the highest variance. The scores in Introductory Microbiology show the least variance. The module Practical Skills for Scientists seems to be the easiest one, since the mean score is higher than the others. Also, the width of the confidence interval (indicated by the length of the line on top of the bar) is small as compared to the others.

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

    © BrainMass Inc. brainmass.com December 24, 2021, 9:16 pm ad1c9bdddf>
    https://brainmass.com/statistics/statistical-figures/bar-charts-confidence-interval-361352

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