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Answer:
90% confidence interval for the population mean iron concentration is [0.771 , 0.832].
Step-by-step explanation:
We are given that a researcher examines 27 water samples for iron concentration. The mean iron concentration for the sample data is 0.802 cc/cubic meter with a standard deviation of 0.093.
Firstly, the pivotal quantity for 90% confidence interval for the population mean iron concentration is given by;
P.Q. = ~
where, = sample mean iron concentration = 0.802 cc/cubic meter
s = sample standard deviation = 0.093
n = number of water samples = 27
= population mean
<em>Here for constructing 90% confidence interval we have used t statistics because we don't know about population standard deviation.</em>
So, 90% confidence interval for the population mean, is ;
P(-1.706 < < 1.706) = 0.90 {As the critical value of t at 26 degree of
freedom are -1.706 & 1.706 with P = 5%}
P(-1.706 < < 1.706) = 0.90
P( <
<
) = 0.90
P( <
<
) = 0.90
<u>90% confidence interval for</u> = [
,
]
= [ ,
]
= [0.771 , 0.832]
Therefore, 90% confidence interval for the population mean iron concentration is [0.771 , 0.832].