Question

Listed below are brain volumes (cm3) of unrelated subjects used in a study. Assume the data is from a simple random sample. Use a 0.01 significance level and the critical values method to test the claim that the population of brain volumes has a mean equal to 1100.0cm3. Be sure to include all steps of a hypothesis test.

963
1027
1272
1079
1070
1173
1067
1347
1100
1204

Answer 1

what steps have you got so far?

Answer 2

I have the critical values of z= -2.575 and z= 2.575

Answer 3

And the formula z= xbar-u/sigma/square root of n

Answer 4

I am not sure if that is the right formula to use

Answer 5

that formulas fine

hmm, all thats left it appears is to find the mean of the sample, and possibly the number of dataelements in the sample.

Answer 6

I am not sure how to find sample mean and standard deviation

Answer 7

not to sure how your material defines 'all steps'

but in general, we state a hypothesis. then compare the results to determine which hypot is most likely

you seem to have the right idea that its a 2 tailed test of equality.

Ho: u = 1100
Ha: u not= 1100

then develop the CI such that:\[\pm2.575=\frac{\bar x-\mu}{\sigma/\sqrt n}\]
\[CI:~\bar x\pm2.575({\sigma/\sqrt n})=\mu\]

Answer 8

standard deviation is given in the information .... and if you dont know how to find the mean of a set of numbers by now, then you might need to review the first chapter of your material

Answer 9

a little error in my thought, i was confusing a precious confidence interval into this setup :)

Answer 10

Okay I know how to find the mean it is just adding the numbers up and dividing but i wasnt sure if thats what it meant by " sample mean"

Answer 11

the data set provided is a sample ... so the sample mean is the mean of the sample data.

Answer 12

Okay thank you, but I still am not sure what the standard deviation is?

Answer 13

what does the information tell us it is?

Answer 14

youre right ... im on a different problem in my head still

Answer 15

I don't know... It tells us the significance level and tells us the population mean

Answer 16

since there is not population sd given, we can subsitute in the sample sd, and use a t distribution. does that sound familiar?

Answer 17

sd?

Answer 18

\[s=\frac{\sum(x-\bar x)^2}{n-1}\]

Answer 19

standard deviation (sd)

Answer 20

is that an 8?

Answer 21

...no

sigma is the variable used for a population sd

s is the variable used to a sample sd

just like: mu is used for a population mean, and xbar is used for a sample mean

Answer 22

thats an s

Answer 23

Thankyou

Answer 24

if sigma (population sd) is known\[\large z=\frac{\bar x-\mu}{\sigma/\sqrt n}\]
if sigma is NOT known, we can substitute the sample sd, s, which gives out setup a t distribution instead of a normal distribution:
\[\large t=\frac{\bar x-\mu}{s/\sqrt n}\]

Answer 25

using excel, we can quickly find the sample mean, variance, and sd

Answer 26

Woah I didn't know you could do that, Haha!

Answer 27

using a t chart .... with a 2 tailed significant level of .01, and dF of 10-1 = 9

http://web.pdx.edu/~stipakb/download/PA551/t-distribution_table.gif

t = 3.25

Answer 28

if out test statisitic of:\[\frac{1130.2-1100.0}{117.45/\sqrt{10}}>3.25\]then we fall in the tails of our hypothesis setup. and reject the null hypot.

Answer 29

How did you get 10-1?

Answer 30

there are 10 data elements listed. so for a t distribution we would need to determine the degrees of freedom as n-1

Answer 31

have you covered t distributions?

Answer 32

No

Answer 33

hmm, yet this is what the information would call for. its similar to a normal distribution, and as the number of data elements in the sample increases it better approximates the normal distribution.

its used in the same manner but with a few tweaks

Answer 34

I am taking an online statistics class, and the modules we have only cover certain things and we are left with the textbook. I am struggling to teach myself because there are very few examples in the textbook

Answer 35

ive used this site to learn a lot of stuff and to teach myself as well. just graduated with a bachelors in math :)

Answer 36

Good for you!

Answer 37

yeah ... now i just need a job lol

http://stattrek.com/probability-distributions/t-distribution.aspx

this sites readable to me and covers the t distribution rather simply.

Answer 38

So it says to not use the t-distribution with sample sizes less than 40?

Answer 39

i read that ..... im gonna do another search.

Answer 40

heres a more simplified rule lol

Answer 41

that doc was from web.pdx.edu