State True or False: Suppose the mean math SAT score of students at Penn State is 610 with a...

Question:

State True or False:

Suppose the mean math SAT score of students at Penn State is {eq}610 {/eq} with a standard deviation of {eq}35 {/eq}, and the histogram roughly follows a normal curve. If I take a random sample of {eq}25 {/eq} Penn State students, then there is approximately a {eq}95\% {/eq} chance that the mean IQ from this sample is between {eq}596 {/eq} and {eq}624 {/eq}.

Confidence Interval:

Confidence Interval gives us the interval estimate of population parameter , it gives us a range between which population parameter found with several times and this several times is called confidence coefficient.

Answer and Explanation:

We have x following normal distribution with mean 610 and standard deviation 35 for a sample size of 25

{eq}\bar x {/eq} follow Normal distribution with mean 610 and standard deviation {eq}\frac{35}{\sqrt{25}} =7 {/eq}

Now we have to find 95% confidence Interval.

{eq}Z_{0.025}=1.96 {/eq}

So P(610-7(1.97) < mu < 610+7(1.97))

596,624 so yess it is true


Learn more about this topic:

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Finding Confidence Intervals with the Normal Distribution

from Statistics 101: Principles of Statistics

Chapter 9 / Lesson 3
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