Question

In a study of 250 adults, the mean heart rate was 70 beats per minute. Assume the population of heart rates is known to be approximately normal with a standard deviation of 12 beats per minute. What is the 99% confidence interval for the mean beats per minute?

Answer 1

last question please someone help!

Answer 2

@mathstudent55 @mathmale @SolomonZelman @ganeshie8

Answer 3

@kirbykirby

Answer 4

CI is:
\[(70-2.576\frac{12}{\sqrt{250}},\ 70+2.576\frac{12}{\sqrt{250}})\]

Answer 5

@kropot72 what does this mean exactly?

Answer 6

Have you not studied the theory of Confidence Intervals? If you calculate out both of the two expressions in brackets, you will have the solution.

Answer 7

@kropot72 i haven't. my online course doesn't explain it well. how exactly do i solve that?

Answer 8

You don't have to solve anything. Just use your calculator to find the two values.

Answer 9

i don't have a calculator to handle that big of an equation @kropot72 is that equation the equation with my problem already in it?

Answer 10

In a study of 250 adults, the mean heart rate was 70 beats per minute. Assume the population of heart rates is known to be approximately normal with a standard deviation of 12 beats per minute. What is the 99% confidence interval for the mean beats per minute?

First of all, Chris, do you know what a "confidence interval" is? If the desired level of confidence is 99%, what is the associated "z-critical value?" I need to know what you already know about this type of problem.

Answer 11

@mathmale I don't know what a CI is, honestly.

Answer 12

this sort of problem becomes quite easy once you've gained a bit of experience with it. However, up front there's a lot of background material to be understood before a "confidence interval" will make sense.

what is your primary source of information about topics about which you must learn in your Statistics course? Book? Online learning materials? Internet searches? Which, if any, of these have you already consulted?

Answer 13

@mathmale I'm in an online course and I have a decent amount of info on probability, I just have no clue how to solve this problem. Can you work through it with me?

Answer 14

Chris, this is a statistics problem, not one in probability.

In a study of 250 adults, the mean heart rate was 70 beats per minute. Assume the population of heart rates is known to be approximately normal with a standard deviation of 12 beats per minute. What is the 99% confidence interval for the mean beats per minute?

The idea here is that we try to ESTIMATE what the true average is of all adult heart rates is, for example, all adults in the USA. You don't have time to measure or otherwise obtain the heart rates of all those adults. Therefore, to get a ball-park estimate of the mean adult heart rate, you take a sample of 250 adults from millions and millions of adults, and then develop an interval (a range of values of x) in which the mean adult heart rate will fall IF you continue to taking many, many samples of 250 adults.

Answer 15

this is inferential statistics: based upon a sample, you make a tentative statement about the entire population.

Does any of this sound at all familiar?

Answer 16

Sort of. How exactly do you set the problem? Is there a formula? @mathmale

Answer 17

Chris, I have no illusions in regard to how much you might learn if I were to type you a few sentences explaining confidence intervals. But I'm going to outline the basic procedure for you.

The center of your confidence interval is the sample mean. You've taken a sample of 250 adults and measured the heart rate of each; the mean of those 250 rates is given and is 70 beats per minute. Repeat: this is the CENTER of y our confidence interval.

Strictly as an example, you might find that in this case the heart rate will be within 67 and 73 beats per minute, written as 70 plus or minus 3 beats, per minute.

Have you ever used the word 'interval' before?

Answer 18

notice how 70 is exactly half way between 67 and 73, and that my 67 and 73 are strictly examples only.

Answer 19

Yes I have @mathmale

Answer 20

okay i understand that @mathmale

Answer 21

So our next task is to determine the "margin of error." In my example, the margin of error is 3, which is how we get 67 from subtracting 3 from 70 and we get 73 by adding 3 to 70.

In this case we have to determine the margin of error.

The formula for margin of error where a population mean is involved is\[(z-critical-value)(population~standard~deviation)/\sqrt{n}\]

Answer 22

Right off the top of my head, the z-critical value for a 99% confidence interval is 2.535 (I will check that); the population standard deviation is 12 heart beats, and the number of samples is 250. Right?

Answer 23

Yes @mathmale, but 99% of what got you 2.535?

Answer 24

@mathmale The appropriate value for z-critical is in my first posting. It is 2.576.

Answer 25

These are my answer choices, I don't see how it really relates to what y'all are talking about


68.9 - 76.3
70 - 72
61.2 - 72.8
68 - 72

Answer 26

@mathmale

Answer 27

Agreed. Chris, either Kropot or I will come back to the question of where we obtain this z-critical-value. For now, accept its value as being 2.58.

What is the population standard deviation?

Answer 28

70? @mathlete

Answer 29

going to answer choices now will teach you little or nothing about the math involved here. I ask that you please bear with me.

Answer 30

The population mean is 70; the standard deviation is 12.

What is n, your sample size?

Answer 31

250 @mathmale

Answer 32

what is the square root of that?

Answer 33

@mathmale 15.811

Answer 34

Please go back to kropot's first post to you, 'way back in this conversation.

You'll see the "margin of error' is 2.58 times the population standard deviation divided by the square root of 250. Right?

Answer 35

Yes, but where did 2.578 come from?

Answer 36

\[2.576\frac{12}{\sqrt{250}}\]

Answer 37

Chris, if you evaluate this, y ou'll get approx. 1.96.

You first subtract that from the sample mean (70), and then you add it to the sampel mean. That's where your confidence interval comes from.

You could do that right now if you want and thus be able to choose the best of the four given possible answers.

Answer 38

So the answer is 68 - 72?!?! @mathmale

Answer 39

In other words, Chris, calculate 70-1.96 and then calculate 70+1.96, and then write the results as an interval:

( something , somthing )

Answer 40

Yes. Does that match any of the answer choices?

Answer 41

All you have to do is to select the CLOSEST answer choice. which one is that?

Answer 42

@kropot72: Are you still with us?

Answer 43

@mathmale here are the choices:

68.9 - 76.3
70 - 72
61.2 - 72.8
68 - 72

Answer 44

chris: where do we get the z-critical value? I'm afraid it'll take a lot of explanation to get that across.

Answer 45

so it WOULD be 68 - 72?

Answer 46

Yes. That answer choice is closest to your calculated interval end points. Yes.

Answer 47

@mathmale @kropot72 thank y'all!

Answer 48

@mathmale I'm still here - part time.

Answer 49

@kropot72: Would you mind taking a stab at explaining where that 2.58 comes from as the approx value of the z-critical value for a 99% confidence interval? that is, if Chris is interested.

Answer 50

@mathmale @kropot72 yeah i just finished and that was right, but i would like to understand it as well. mathmale are you a real life teacher or what?

Answer 51

@mathmale Certainly. Just give me five minutes to finish my meal please :)

Answer 52

I've been tutoring almost 45 years; I recently retired from a college teaching career.

Answer 53

I'm curious what approach kropot72 will use to explain the derivation of the z critical value. I will leave the lion's share of that explanation to him.

Basically, we're working with a standard normal curve that looks like this: