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: 85 + / - 9.79

= (75.21, 94.79)

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

Step-by-step 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)

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

Step-by-step 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