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JulijaS [17]
3 years ago
15

Find the sample size necessary to estimate the mean IQ score of statistics students such that it can be said with 99​% confidenc

e that the sample mean is plus or minus8 IQ points of the true mean. Assume that the standard deviation is 13 and determine the required sample size. nequals nothing ​(Round up to the nearest​ integer.)
Mathematics
1 answer:
quester [9]3 years ago
4 0

Answer: 18

Step-by-step explanation:

The formula to find the minimum sample size is given by :_

n=(\dfrac{z^*\cdot \sigma}{E})^2

, where \sigma = population standard deviation.

z*= critical z-value.

E= Margin of error.

Given : \sigma= 13

E= ± 8

We know that critical value corresponding to 99% confidence level = z*=2.576  [Using z-table]

Then, the required sample size would be :

n=(\dfrac{(2.576)\cdot (13)}{8})^2

\Rightarrow\ n=(4.186)^2

\Rightarrow\ n=17.522596\approx18 [Round to next integer.]

Hence, the required minimum sample size = 18

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Answer: In degrees , The measure of \theta=65.5^{\circ}

In radians , the measure of  \theta =\dfrac{8}{7}\text{ radians}.

Step-by-step explanation:

We know that the formula for length of arc is given by :-

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To convert it into degrees we multiply it with \dfrac{180^{\circ}}{\pi}

The measure of \theta =\dfrac{8}{7}\times\dfrac{180^{\circ}}{\pi}

=(\dfrac{8\times180}{7\times3.14})^{\circ}=65.5141037307^{\circ}

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Hence, the measure of \theta=65.5^{\circ}

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