# Bar Charts and Confidence Interval

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.

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## 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 Ì…-(z_(Î±/2) s)/âˆšn,x Ì…+(z_(Î±/2) s)/âˆšn)

where,Sample Size,n=27

Mean,x Ì…=61.074

Standard Deviation,s=13.182

z_(Î±/2) for 95% confidence=1.96

Thus the 95% confidence interval for the mean score is given as

(61.074-(1.96Ã—13.182)/âˆš27,61.074+(1.96Ã—13.182)/âˆš27)

=(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 Ì…-(z_(Î±/2) s)/âˆšn,x Ì…+(z_(Î±/2) s)/âˆšn)

where,Sample Size,n=21

Mean,x Ì…=77.571

Standard Deviation,s=11.788

z_(Î±/2) for 95% confidence=1.96

Thus the 95% confidence interval for the mean score is given as

(77.571-(1.96Ã—11.788)/âˆš21,77.571+(1.96Ã—11.788)/âˆš21)

=(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 Ì…-(z_(Î±/2) s)/âˆšn,x Ì…+(z_(Î±/2) s)/âˆšn)

where,Sample Size,n=23

Mean,x Ì…=42.522

Standard Deviation,s=13.182

z_(Î±/2) for 95% confidence=1.96

Thus the 95% confidence interval for the mean score is given as

(42.522-(1.96Ã—11.630)/âˆš23,42.522+(1.96Ã—11.630)/âˆš23)

=(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 Ì…-(z_(Î±/2) s)/âˆšn,x Ì…+(z_(Î±/2) s)/âˆšn)

where,Sample Size,n=30

Mean,x Ì…=59.067

Standard Deviation,s=4.968

z_(Î±/2) for 95% confidence=1.96

Thus the 95% confidence interval for the mean score is given as

(59.067-(1.96Ã—4.968)/âˆš30,59.067+(1.96Ã—4.968)/âˆš30)

=(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.

https://brainmass.com/statistics/statistical-figures/bar-charts-confidence-interval-361352