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1jennator
31.03.2020 •
Mathematics
In 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. Determine the 90% confidence interval for the mean waste recycled per person per day for the population of Washington. 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.
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Ответ:
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. =
~ ![t_n_-_1](/tpl/images/0572/0097/5cbec.png)
where,
= sample mean waste recycled per person per day = 2.3 pounds
s = sample standard deviation = 0.39 pounds
n = sample of residents = 10
Here for constructing 90% confidence interval we have used t statistics because we don't know about population standard deviation.
So, 90% confidence interval for the population mean,
is ;
P(-1.833 <
< 1.833) = 0.90 {As the critical value of t at 9 degree of
freedom are -1.833 & 1.833 with P = 5%}
P(-1.833 <
< 1.833) = 0.90
P(
<
<
) = 0.90
P(
<
<
) = 0.90
90% confidence interval for
= [
,
]
= [
,
]
= [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].
Ответ:
16 divided by 3 is 5.3 repeating so he would have 5 containers filled completely & 1 filled partially. 6 total containers