Question

Data on the blood cholesterol levels of 10 rats (milligrams per deciliter of blood) give x = 85 and s = 12. A 99% confidence interval for the mean blood cholesterol of rats is

Answer 1

Answer: 85 +/- 9.79

= ( 75.21, 94.79)

Therefore at 99% confidence interval (a,b) = ( 75.21, 94.79)

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 gain x = 85

Standard deviation r = 12

Number of samples n = 10

Confidence interval = 99%

z(at 99% confidence) = 2.58

Substituting the values we have;

85 +/-2.58(12/√10)

85+/-2.58(3.795)

85 +/- 9.79

= ( 75.21, 94.79)

Therefore at 99% confidence interval (a,b) = ( 75.21, 94.79)

Answer 2

99% confidence interval for the mean blood cholesterol of rats is between 72.66 milligrams per deciliter of blood and 97.34 milligrams per deciliter of blood

Explanation:

Confidence Interval = mean (x) + or - margin of error (e)

e = t×s/√n

s = 12, n = 10, degree of freedom = n-1 = 10-1 = 9, t-value corresponding to 9 degrees of freedom and 99% confidence level is 3.250

e = 3.250×12/√10 = 12.34

Lower bound = x - e = 85 - 12.34 = 72.66

Upper bound = x + e = 85 + 12.34 = 97.34

99% confidence interval is (72.66, 97.34) milligrams per deciliter of blood