Confidence Interval refers to the range of numbers within which the results of a given survey conducted at a given degree of confidence lie. Whereas, the degree of confidence is a percentage expressing the rate at which the results of the survey will match if the survey is to be repeated over and over again. For instance, a 98% degree of confidence indicates that should one repeat an experiment over and over again, 98% of the obtained results will match. On the other hand, given results on an experiment with a 98% degree of confidence that sought to determine the height of a certain species of monkey in a park; the average height (µ) was 101.83 cm and the standard deviation 1.2. The following calculation determines the confidence interval having measured 35 monkeys (n).
Obtain the alpha level of the population by subtracting the degree of confidence from one and dividing by 2. (1-0.98)/2 = 0.01;
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Subtract the alpha level from 1 and determine the z score of the area. 1-0.01 = 0.99. the Z score (Z) for the given area is obtained by using a look-up table Z = 2.33;
Using the formula Z×σ/√(n) where n is the sample size gives 2.33 ×1.2/√(35) = 0.4726;
The upper limit and the lower limit are calculated as follows (µ-0.4726) to (µ+0.4726) giving (101.83 -0.4726) to (101.83 + 0.4726) resulting to 101.3574 to 102.3026.
The confidence interval for the experiment is 101.3574cm to 102.3026 cm meaning that if the monkeys were to be measured over and over again, 98% of the result would be between 101.3574cm to 102.3026 cm.
The table below is a screen capture of the Z score lookup table used in step 2.
Fig 1. Screen capture of Z score lookup table.
Question 2
Response on Alyson Davis
The working of the confidence interval is correct. However, the conclusion is wrong. The 32.86 and 39.14 minutes depicted by the calculated confidence interval provide a 95% confidence on the actual delivery time and not the mean delivery time as stated.
Response on JudnaDesrivieres
The estimation of the confidence interval is inaccurate. A better approach would have been to use the t distribution given the small sample size of 10 individuals. Furthermore, the question does not specify the degree of confidence. Therefore, one does not have any certainty degree of obtaining stated values.
