Math probability Please help
2 answers:
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Answer:
80% confidence interval for the mean waste recycled per person per day for the population of New York is [2.495 , 3.305].
Step-by-step explanation:
We are given that a random sample of 11 residents of the state of New York, the mean waste recycled per person per day was 2.9 pounds with a standard deviation of 0.98 pounds.
Firstly, the pivotal quantity for 80% confidence interval for the true mean waste recycled per person per day for the population of New York is given by;
P.Q. = ~
where, = sample mean waste recycled per person per day = 2.9 pounds
s = sample standard deviation = 0.98 pounds
n = sample of residents = 11
= true mean waste recycled per person per day
<em>Here for constructing 80% confidence interval we have used t statistics because we don't know about population standard deviation.</em>
So, 80% confidence interval for the true mean, is ;
P(-1.372 < < 1.372) = 0.80 {<u>As the critical value of t at 10 degree of </u>
<u>freedom are -1.372 & 1.372 with P = 10%</u>}
P(-1.372 < < 1.372) = 0.80
P( <
<
) = 0.80
P( < -
<
) = 0.80
P( <
<
) = 0.80
<u>80% confidence interval for</u> = [
,
]
= [ ,
]
= [2.495 , 3.305]
Therefore, 80% confidence interval for the mean waste recycled per person per day for the population of New York is [2.495 , 3.305].