Mercury is a toxic element and serves no beneficial physiological function in ma
ID: 3181660 • Letter: M
Question
Mercury is a toxic element and serves no beneficial physiological function in man; a maximum acceptable concentration of 0.001 mg/L (1 µg/L) in drinking water has therefore been established. A researcher pull samples of drinking water from the county X. The results are given in table below.
Position
Mercury µg/L
1
0.80
2
0.67
3
0.88
4
1.06
5
0.98
6
0.85
7
0.90
8
1.01
9
0.84
10
0.81
11
0.76
12
0.90
13
0.84
14
0.67
15
1.01
16
0.87
17
0.94
18
0.94
19
0.94
20
1.07
21
0.96
22
0.80
23
0.80
24
0.76
25
1.09
26
0.87
27
0.82
28
0.89
29
0.85
30
0.95
31
0.97
With confidence of 99.99% determine whether the level of mercury in water in County X is safe.
Position
Mercury µg/L
1
0.80
2
0.67
3
0.88
4
1.06
5
0.98
6
0.85
7
0.90
8
1.01
9
0.84
10
0.81
11
0.76
12
0.90
13
0.84
14
0.67
15
1.01
16
0.87
17
0.94
18
0.94
19
0.94
20
1.07
21
0.96
22
0.80
23
0.80
24
0.76
25
1.09
26
0.87
27
0.82
28
0.89
29
0.85
30
0.95
31
0.97
Explanation / Answer
Confidence Interval
CI = x ± t a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
ta/2 = t-table value
CI = Confidence Interval
Mean(x)=0.887097
Standard deviation( sd )=0.1058
Sample Size(n)=31
Confidence Interval = [ 0.887097 ± t a/2 ( 0.1058/ Sqrt ( 31) ) ]
= [ 0.887097 - 4.482 * (0.019) , 0.887097 + 4.482 * (0.019) ]
= [ 0.802,0.972 ]
Interpretations:
1) We are 99.99% sure that the interval [0.802 , 0.972 ] contains the true population mean
2) If a large number of samples are collected, and a confidence interval is created
for each sample, 99.99% of these intervals will contains the true population mean
whether the level of mercury in water in County X is safe