Question

A sample of 80 Valencia oranges showed a mean weight of 5.5 ounces with a standard deviation of 0.2 ounces. Obtain a 95% confidence interval for the weight of Valencia oranges. [5.495, 5.505 ] [0.195, 0.205] [ 5.456,5.544] [0.156, 0.244 )

Answer 1

[ 5.456, 5.544]

Explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

x+/-zr/√n

Given that;

Mean x = 5.5 ounces

Standard deviation r = 0.2 ounces

Number of samples n = 80

Confidence interval = 95%

z value (at 95% confidence) = 1.96

Substituting the values we have;

5.5+/-1.96(0.2/√80)

5.5+/-1.96(0.022360679774)

5.5+/-0.043826932358

5.5+/-0.044

= ( 5.456, 5.544) ounces

Therefore the 95% confidence interval (a,b) = ( 5.456, 5.544) ounces