Homework SourseStatistic question five Six healthy threeyearold female Suff
Statistic question five
Six healthy three-year-old female Suffolk sheep were injected with the antibiotic Gentamicin, at a dosage of 10 mg/kg body weight. Their blood serum concentration (g/ml) of Gentamicin 1.5 hours after the injection were as follows:
33, 26, 34, 21, 23, 25
(a) Construct a 90% confidence interval for the population mean. Be sure to interpret this confidence interval in the context of this setting.
(b) Construct a 99% confidence interval for the population mean. Be sure to interpret this confidence interval in the context of this setting.
Solution
A)
Note that
Lower Bound = X - t(alpha/2) * s / sqrt(n)
Upper Bound = X + t(alpha/2) * s / sqrt(n)
where
alpha/2 = (1 - confidence level)/2 = 0.05
X = sample mean = 27
t(alpha/2) = critical t for the confidence interval = 2.015048373
s = sample standard deviation = 5.329165038
n = sample size = 6
df = n - 1 = 5
Thus,
Lower bound = 22.61601539
Upper bound = 31.38398461
Thus, the confidence interval is
( 22.61601539 , 31.38398461 ) [ANSWER]
Thus, we are 90% confident that the true mean is between 22.61601539 and 31.38398461.
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b)
Note that
Lower Bound = X - t(alpha/2) * s / sqrt(n)
Upper Bound = X + t(alpha/2) * s / sqrt(n)
where
alpha/2 = (1 - confidence level)/2 = 0.005
X = sample mean = 27
t(alpha/2) = critical t for the confidence interval = 4.032142984
s = sample standard deviation = 5.329165038
n = sample size = 6
df = n - 1 = 5
Thus,
Lower bound = 18.22757894
Upper bound = 35.77242106
Thus, the confidence interval is
( 18.22757894 , 35.77242106 ) [ANSWER]
Thus, we are 99% confident that the true mean is between 18.22757894 and 35.77242106.
