Sevilla cuts the four corners off a rectangular piece of wood as shown in the diagram.
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Answer:
A 95% confidence interval for the population mean is [3315.13, 22480.87] .
Step-by-step explanation:
We are given that for quality control purposes, we collect a sample of 200 items and find 24 defective items.
Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;
P.Q. = ~
where, = sample proportion of defective items = 12,898
s = sample standard deviation = 7,719
n = sample size = 5
= population mean
<em> Here for constructing a 95% confidence interval we have used a One-sample t-test statistics as we don't know about population standard deviation. </em>
<u>So, 95% confidence interval for the population mean, </u><u> is ;
</u>
P(-2.776 < < 2.776) = 0.95 {As the critical value of t at 4 degrees of
freedom are -2.776 & 2.776 with P = 2.5%}
P(-2.776 < < 2.776) = 0.95
P( <
<
) = 0.95
P( <
<
) = 0.95
<u>95% confidence interval for</u> = [
,
]
= [ ,
]
= [3315.13, 22480.87]
Therefore, a 95% confidence interval for the population mean is [3315.13, 22480.87] .