A physicist examines 10 water samples for iron concentration

A physicist examines 10 water samples for iron concentration. The mean iron concentration for the sample data is 0.711 cc/cubic meter with a standard deviation of 0.0816. Determine the 90% confidence interval for the population mean iron concentration. Assume the population is approximately normal.

Step 1 of 2: Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.

Step 2 of 2: Construct the 90% confidence interval. Round your answer to three decimal places. Lower endpoint? Upper endpoint?

Solution

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)=0.711
Standard deviation( sd )=0.0816
Sample Size(n)=10
Confidence Interval = [ 0.711 ± t a/2 ( 0.0816/ Sqrt ( 10) ) ]
= [ 0.711 - 1.833 * (0.026) , 0.711 + 1.833 * (0.026) ]
= [ 0.664,0.758 ]

[ANSWERS]
a.
Crtical Point = 1.833

b.
Lower = 0.664
upper = 0.758