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# Bar Charts and Confidence Interval

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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.

##### Solution Summary

This solution is comprised of detailed step-by-step calculations of confidence interval estimates and construction of bar charts in EXCEL.

##### Solution Preview

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)

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