In a classroom of 28 students: 19 of the students have brown eyes 13 of the students wear glasses 7 of the students do not have
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Answer:
With 90% confidence, it can be said that the population mean price lies in the first interval. With 95% confidence, it can be said that the population mean price lies in the second interval. The 95% confidence interval is wider than the 90%.
Step-by-step explanation:
We are given that a random sample of 60 home theater systems has a mean price of$131.00. Assume the population standard deviation is$18.80.
- Firstly, the pivotal quantity for 90% confidence interval for the population mean is given by;
P.Q. = ~ N(0,1)
where, = sample mean price = $131
= population standard deviation = $18.80
n = sample of home theater = 60
= population mean
<em>Here for constructing 90% confidence interval we have used One-sample z test statistics as we know about the population standard deviation.</em>
<u>So, 90% confidence interval for the population mean, </u><u> is ;</u>
P(-1.645 < N(0,1) < 1.645) = 0.90 {As the critical value of z at 5% level
of significance are -1.645 & 1.645}
P(-1.645 < < 1.645) = 0.90
P( <
<
) = 0.90
P( <
<
) = 0.90
<u>90% confidence interval for</u> = [
,
]
= [ ,
]
= [127.01 , 134.99]
Therefore, 90% confidence interval for the population mean is [127.01 , 134.99].
- Now, the pivotal quantity for 95% confidence interval for the population mean is given by;
P.Q. = ~ N(0,1)
where, = sample mean price = $131
= population standard deviation = $18.80
n = sample of home theater = 60
= population mean
<em>Here for constructing 95% confidence interval we have used One-sample z test statistics as we know about the population standard deviation.</em>
<u>So, 95% confidence interval for the population mean, </u><u> is ;</u>
P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 2.5% level
of significance are -1.96 & 1.96}
P(-1.96 < < 1.96) = 0.95
P( <
<
) = 0.95
P( <
<
) = 0.95
<u>95% confidence interval for</u> = [
,
]
= [ ,
]
= [126.24 , 135.76]
Therefore, 95% confidence interval for the population mean is [126.24 , 135.76].
Now, with 90% confidence, it can be said that the population mean price lies in the first interval. With 95% confidence, it can be said that the population mean price lies in the second interval. The 95% confidence interval is wider than the 90%.