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Answer:
90% confidence interval for the mean waste recycled per person per day for the population of Washington is [2.074 , 2.526].
Step-by-step explanation:
We are given that a a random sample of 10 residents of the state of Washington, the mean waste recycled per person per day was 2.3 pounds with a standard deviation of 0.39 pounds.
Firstly, the pivotal quantity for 90% confidence interval for the mean waste recycled per person per day for the population of Washington is given by;
P.Q. = ~
where, = sample mean waste recycled per person per day = 2.3 pounds
s = sample standard deviation = 0.39 pounds
n = sample of residents = 10
= population mean waste recycled per person per day
<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(-1.833 < < 1.833) = 0.90 {<u>As the critical value of t at 9 degree of</u>
<u>freedom are -1.833 & 1.833 with P = 5%</u>}
P(-1.833 < < 1.833) = 0.90
P( <
<
) = 0.90
P( <
<
) = 0.90
<u>90% confidence interval for</u> = [
,
]
= [ ,
]
= [2.074 , 2.526]
Therefore, 90% confidence interval for the mean waste recycled per person per day for the population of Washington is [2.074 , 2.526].