Calcium levels in the blood of an individual tend to vary normally over time. Ca
ID: 3364057 • Letter: C
Question
Calcium levels in the blood of an individual tend to vary normally over time. Calcium levels can be measured using a simple blood test. The following are the calcium levels in mg/dl of an individual taken at six different times. 9.2 9.8 8.7 9.5 9.0 9.8 Find a 90% confidence interval for this individual’s mean calcium level. Calcium levels in the blood of an individual tend to vary normally over time. Calcium levels can be measured using a simple blood test. The following are the calcium levels in mg/dl of an individual taken at six different times. 9.2 9.8 8.7 9.5 9.0 9.8 Find a 90% confidence interval for this individual’s mean calcium level. Calcium levels in the blood of an individual tend to vary normally over time. Calcium levels can be measured using a simple blood test. The following are the calcium levels in mg/dl of an individual taken at six different times. 9.2 9.8 8.7 9.5 9.0 9.8 Find a 90% confidence interval for this individual’s mean calcium level.Explanation / Answer
9.2 9.8 8.7 9.5 9.0 9.8
n = 6
Mean x' = (9.2 + 9.8 + 8.7 + 9.5 + 9.0 + 9.8) / 6
= 56 / 6
= 28/3
= 9.3333.
Sum of the squares of differences = (9.2 - 28/3)2 + (9.8 - 28/3)2 + (8.7 - 28/3)2 + (9.5 - 28/3)2 + (9.0 - 28/3)2 + (9.8 - 28/3)2 = 0.9933
Sample standard deviation s = (0.9933/5) = 0.4457.
z for 90% = 1.645
Let the interval be (a,b).
a = x' - z s / n
= 9.3333 - 1.645 * 0.4457 / 6
= 9.0340.
b = x' + z s / n
= 9.3333 + 1.645 * 0.4457 / 6
= 9.6326.
The interval is (9.0340, 9.6326).