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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).