Question

I have a math question please help!

Answer 1

Carl conducted an experiment to determine if there is a difference in the mean body temperature between men and women. He found that the mean body temperature for a sample of 100 men was 91.1 with a population standard deviation of 0.52 and the mean body temperature for a sample of 100 women was 97.6 with a population standard deviation of 0.45.

Assuming the population of body temperatures for men and women is normally distributed, calculate the 98% confidence interval and the margin of error for the mean body temperature for both men and women. Using complete sentences, explain what these confidence intervals mean in the context of the problem.

Answer 2

@TuringTest @dan815 @undeadknight26 @paki @Skyz

Answer 3

what part are you stuck at?

Answer 4

Honestly I don't understand any of it.

Answer 5

It's the last question on an exam of 5 questions, and It has nothing to do with what im learning, this is like statistics and i'm taking Alg 2

Answer 6

it is stats

Answer 7

you know how to find a zscore?

Answer 8

No

Answer 9

a confidence interval is just some spread about the mean, so we start with the mean, then add/subtract the required number of standard deviations that are attributed to the percentage demanded

Answer 10

the hardest part is just looking stuff up on a table, if you got a stats calc like a ti83 its not even that hard

Answer 11

I use my phone as a calculator, don't even have a real one XD

Answer 12

then youd need a table

Answer 13

What type of table ?

Answer 14

a z table of course :)

Answer 15

I don't know what that is XD I didn't even know what a Zscore was

Answer 16

a confidence interval is formulated as:
\[mean\pm z(SE)\]
SE is the standard error, or the margin of error and is just the standard deviation divided by the sqrt of the sample size

Answer 17

we have all the info needed, and the table is used to find the value of z

Answer 18

Okay So how do I plug it in?

Answer 19

98% leaves 2% free, half in each tail. so a zscore related to .0100 is needed

Answer 20

a stat calculator will have an invnorm function that gives us the z score associated with a probability area.

http://www.wolframalpha.com/input/?i=invnorm%28.0100%29

Answer 21

Okay I get the first half of that, because the bell curve is symmetrical, so 50% of the 2% goes in each side, so 1% and 1% but the zscore thing lost me again

Answer 22

z score is simply the number of standard deviations that fit between some x and the mean

Answer 23

but the mean is zero?

Answer 24

\[z=\frac{x-mean}{sd}\]
the confidence interval is finding a low and high x value associated with whatever probability is attributed to the confidence interval

in this case we want a zscore that has a value of .0100 associated with it

Answer 25

the mean is not 0, its stated for each group

Answer 26

But that link you gave me said the mean was 0

Answer 27

the mean of a normal distribution is 0 with a standard deviation of 1

we can rework any 'normally' distributed data by subtracting the mean from all the points, and dividing out the standard deviation

Answer 28

Okay

Answer 29

I think the standard deviation with my problem was .45

Answer 30

mean sample of 100 men
was 91.1 with a
population standard deviation of 0.52 and

the mean body temperature for a sample of 100 women
was 97.6 with a
population standard deviation of 0.45.

Answer 31

if we do just the women:

\[\pm z=\frac{\pm x-mean}{\sigma/\sqrt{n}}\]
\[\pm z(\sigma/\sqrt n)=\pm x-mean\]
\[mean\pm z(\sigma/\sqrt n)=\pm x\]

Answer 32

we are given the mean, n, sigma ... and are told to use a z that gives us a 1% tail: the invnorm function says z=2.326

Answer 33

I'm going to admit, that just looks like a bunch of fancy symbols :/

Answer 34

it is :) but thats generality for you

Answer 35

XD I hate math.

Answer 36

So back to the actual question it wants me to explain the confidence intervals?

Answer 37

a confidence interval is dependant upon the central limit thrm.

the central limit thrm says that for a large number of samples, the mean of the sample means will be normally distributed. so we would expect that for a specific sample, we can be p% confident that the true population mean is somewhere within the interval

Answer 38

so, in this case, we are 98% confident that the true population mean, is someplace between the interval we found.

Answer 39

Okay

Answer 40

the interval being the zscore ? or the Standard deviation>?

Answer 41

the interval being the confidence interval that we find using the formulas ive already posted

Answer 42

the zscore and the standard deviation are only parts of the formula

Answer 43

when i use a hammer to build a wall, the hammer isnt the wall.

Answer 44

Okay so do you mind going over that again in simple terms that I can comprehend XD?

Answer 45

Well obviously a hammer isnt a wall

Answer 46

i can only use terms I can comprehend.

Answer 47

do we agree that the mean, the standard deviation, the sample size, and the desired percentage of the confidence interval are stated in the problem?

Answer 48

Yes :D

Answer 49

Because I like agreeing

Answer 50

then we use them to fill in the formula for the confidence interval:\[mean\pm z(sd/\sqrt n)=(x_1,x_2)\]

Answer 51

everything but z is given outright; we use the 1% tail to obtain the value of z

Answer 52

invnorm(.0100) = 2.326

or if by table it might have been determined as 2.33

Answer 53

so, we simply use the values with the formula

Answer 54

calculate the 98% confidence interval, use the formula

and the margin of error: thats the z(sd/sqrt(n)) part of the equation

Answer 55

Okay...

Answer 56

My issue right now is , I dont know what the symbols stand for...

Answer 57

Sd is probably standard deviation, Z is the zscore, square root of N??? and x and x2?

Answer 58

\[mean\pm z(sd/\sqrt n)=(x_1,x_2)\]
sqrt n, n is the sample size, in this case 100 people sampled

x1 and x2 are the endpoint of the interval

Answer 59

x1 = mean - E (E stands for margin of error)
x2 = mean + E

Answer 60

OKay that does help :) But I don't know the margin of error do I?

Answer 61

would you mind plugging it into the formula?

Answer 62

you should, all i did was rename a part of the formula for simplicities sake

Answer 63

what are we +/- ing in the formula?

Answer 64

starts with a z and ends with a sqrtn

Answer 65

the mean?

Answer 66

Sorry man I still don't understand any of this :/ Thanks so much for trying to explain to me, but I'm just not a math guy. I'm trying to understand, and thank you so much for your time. But I don't think I'll ever get it.

Answer 67

\[mean\pm E~~\to~~ mean\pm z(sd/\sqrt n)\]

Answer 68

do you agree that E is simpler to write up?

Answer 69

yes :o

Answer 70

Much easier.

Answer 71

the formula doesnt change because we make writing it simpler

Answer 72

\[E = z(SE)\]
SE means standard error
can you tell from this how we calculate the standard error?

Answer 73

Multiply z x SE ?

Answer 74

or figure out what e is

Answer 75

and then divide by z

Answer 76

standard error is already define as SE, comparing it to the formula already stated over and over again.

z(SE) = z(sd/sqrt(n))

therefore the calculation for standard error is sd/sqrt(n)

Answer 77

Yeah That doesn't make any sense.

Answer 78

its just naming parts of the formula so that they can be discussed in their own right

Answer 79

I'm on a timed test with this question and i got 5 minutes left. So I'm just going to BS it and thank you for your time XD i'm sorry i dont understand any of this.

Answer 80

a confidence interval is the formula:

mean +- E

E is defined as the margin of error



E = z(SE)

ok, good luck with it :)

Answer 81

You're trying so hard to explain, but I have learning issues and I dont really understand things by just seeing words

Answer 82

How do I medal you or something?

Answer 83

if you feel i did well, there is a best response button net to everything i posted. it gives a medal

Answer 84

*next to

Answer 85

Okay I clicked that :D thanks for your time, sorry I dont understand this

Answer 86

it takes time and lots of practice :) again, good luck