7th grade math pls help
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Answer:
95% confidence interval for the mean of the 800 instructors is [126.80 , 133.20].
Step-by-step explanation:
We are given that there were 800 math instructors at a mathematics convention.
Forty instructors were randomly selected and given an IQ test. The scores produced a mean of 130 with a standard deviation of 10.
Firstly, the pivotal quantity for 95% confidence interval for the population mean is given by;
P.Q. = ~
where, = sample mean score = 130
s = sample standard deviation = 10
n = sample of instructors = 40
= population mean of 800 instructors
<em>Here for constructing 95% confidence interval we have used One-sample t test statistics as we know don't about population standard deviation.</em>
So, 95% confidence interval for the population mean, is ;
P(-2.0225 < < 2.0225) = 0.95 {As the critical value of t at 39 degree of
freedom are -2.0225 & 2.0225 with P = 2.5%}
P(-2.0225 < < 2.0225) = 0.95
P( <
<
) = 0.95
P( <
<
) = 0.95
<u><em /></u>
<u><em>95% confidence interval for</em></u> = [
,
]
= [ ,
]
= [126.80 , 133.20]
Therefore, 95% confidence interval for the mean of the 800 instructors is [126.80 , 133.20].