Question

In a study of 225 adults, the mean heart rate was 72 beats per minute. Assume the population of heart rates is known to be approximately normal with a standard deviation of 10 beats per minute. What is the 90% confidence interval for the mean beats per minute?

Answer 1

@mathmale

Answer 2

So we're trying to come up with a ballpark estimate of the "true mean adult heart rate," based upon sampling 225 adults. In other words, we want a 90% confidence interval; we can't say for certain that the true mean adult heart rate is so and so, but can state with 90% confidence that if we took repeated samples of size 225, our confidence interval would contain this true mean 90% of the time. Hope this makes sense.

Answer 3

What would first few steps be, towards computing that interval?

Answer 4

lol I dont know what would they be?

Answer 5

We're dealing with the concepts of mean and standard deviation

Answer 6

is there a formula for this

Answer 7

in sampling. Right up front, let's assert that if a sample is drawn from a population, we assume that the population mean is the same as that of the sample. In other words, if we've found that the sample mean is 72, then we're going to use 72 as the center point of our confidence interval.

Answer 8

When dealing with population and sample proportions, the rule is different. But that's a nother study.

Answer 9

We are told that the population std. dev. is 10. Another rule applies here: If the population std. dev. (denoted by sigma) is known, then the sample std. dev. is S=(sigma)/Sqrt(n).
Have you seen this before?

Answer 10

Would this come under conditional probability or normal distribution

Answer 11

Definitely "normal distribution."
What I'm going to do is simply find the confidence interval, and then go back and discuss how we did that and why. OK with you?

Answer 12

ok fine with me

Answer 13

More specifically, woohoo, we're dealing with descriptive statistics. We have a sample of size n=225, know that the std. dev. of the population is 10, and are responding to a request for a 90% confidence interval by which we'll estimate the true population mean.

Answer 14

Where would you normally look up formulas for something like this? Have you a book, class notes or any other reference that might list "confidence interval for population mean"?

Answer 15

hold on i'll check

Answer 16

are you asking for the z formula?

Answer 17

The formula we need here looks like this:

Confidence interval when population std. is known :is

(sample mean) (plus or minus) (z-critical value)(population standard dev) / Sqrt(n).

Answer 18

Mind writing that down on paper?

Answer 19

Once you have that written down, let's plug in the knows:

Answer 20

72 (plus or minus) (z critical value) (10) / Sqrt (225)

Answer 21

before I type anything further: any questions yet?

Answer 22

whats the z critical value

Answer 23

It's a multiplier whose value depends on the level of confidence you want in your confidence interval. In this problem, you want a 90% confidence interval. For that level, the z-critical value is 1.28. I will do a quick Internet search and find further explanations of this concept.

Answer 24

\[72\pm zcritical \frac{ 10 }{ \sqrt{225} }\]

Answer 25

is this how it would look like

Answer 26

woohoo: Please see http://www.math.armstrong.edu/statsonline/5/5.3.2.html.
You've done a great job of typing in that formula.

If you'll look at the web page whose URL I've given you, you'll see that the z critical value for a 90% confidence interval is 1.645 (I was mistaken in saying it was 1.28).

Answer 27

1.645 now i jst plug it in and solve it?

Answer 28

So please take the formula you've just typed out and substitute 1.645 for the z critical value.

Calculate the confidence interval, writing it in the form 72 (plus or minus) 1.645(10)/Sqrt(225).

Answer 29

yes, plug in 1.645 and calculate the C. I.

Answer 30

BRB

Answer 31

BRB="be right back" I'm back. How are your calculations going?

Answer 32

70.9 – 73.1

Answer 33

Please write that in this interval notation/format:

(70.9,73.1).

Answer 34

I'd bet you'll be asked to interpret what this stands for.
Here's one possible wording?
"If samples of size n=225 are repeatedly chosen from the population of adults, a 90% confidence interval for the true mean population heart rate would be (70.9,73.1)."

Answer 35

this is one of the options i got the same thing is it right?

Answer 36

We do NOT actually know the mean population heart rate, but have a "good" estimate for it.

Answer 37

Before I answer your questin, would u please type out the answer options for me?

Answer 38

70.7 – 73.3

70.9 – 73.1

70.7 – 73.1

70.9 – 73.3

Answer 39

OK. In that case, go ahead and choose 70.9 - 73.3. This indicates that "the true population mean heart rate is between 70.9 and 73.3 at a 90% level of confidence."

Answer 40

Thank You

Answer 41

Hope you'll take careful notes on this discussion, as you'll definitely be tested on this material later on.

Answer 42

This work was aimed at finding a 90% confidence interval for a population mean.

There's another common situation: confidence intervals for a population proportion.

Answer 43

that answer is wrong for anyone in the future

Answer 44

It was almost correct...
Its 70.9-73.1