**Stats200_week_5 homework**

**Why is a 99% confidence interval wider than a 95% confidence interval?**

Solution)

The definition of a confidence interval is that it contains the true population mean. If I have a 95% confidence interval, that means I am 95% certain that the true population mean is in the interval. If I want to be even more certain, I have to widen the interval. If I can be less certain, I can narrow the interval.

So the widest interval will be 99%, and the narrowest would be 90%.

Example:

you're trying to figure out where in the city Comet Donuts is in, but you really don't know for sure. A desperately hungry person hands you a map and asks you to show him where it is. If someone forces you to be 99% accurate, are you going to draw a wide or narrow circle on the map? You can't afford to be wrong - at 99% you're saying that you'll be wrong one time out of 100! So you draw a big circle.

If the person asking doesn't even like donuts, they're just asking for the heck of it, you can be 90% accurate, so you can take a chance and draw a small circle. You'll be wrong 10% of the time.

*12.** A person claims to be able to predict the outcome of flipping a coin. This person is correct 16/25 times. Compute the 95% confidence interval on the proportion of times this person can predict coin flips correctly. What conclusion can you draw about this test of his ability to predict the future?*

Solution)

WE HAVE GIVEN THAT n = 25 and p = 16/25

And we need to construct the 95% C.I. for the proportion of times this person can predict coins flips correctly as,

ṕ± 1.96 * √ (ṕq^/n)

=.64± 1.96 * √ (.64*.36/25)

= .64 ± .1882

So the 95% C.I. is,

(0.4518, 0.8282)

So We Are 95 Out Of 100 Attempts are confident that the values of the samples are lies b/w (.4518,.8282)

*15.** You take a sample of 22 from a population of test scores, and the mean of your sample is 60.*

*(a) You know the standard deviation of the population is 10. What is the 99% confidence interval on the population mean?*

Solution)

We have given that n = 22, sample mean =60 and σ = 10

The 99% C.I. for the population mean is,

= sample mean ± 2.58 *σ /√n

= 60 ± 2.58 * 10 / √22

= 60 ± 5.501

So, (54.499, 65.501)

**Category:**Business, General Business

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