Question

You measure the weights of 24 male runners. You do not actually choose an SRS, but you are willing to assume that these runners are a random sample from the population of male runners in your town or city. Here are their weights in kilograms:

67.8 61.9 63.0 53.1 62.3 59.7 55.4 58.9
60.9 69.2 63.7 68.3 64.7 65.6 56.0 57.8
66.0 62.9 53.6 65.0 55.8 60.4 69.3 61.7

Answer 1

a) Suppose that the standard deviation of the population is known to be sigma = 4.5 kg. What is sx, the standard error of x?
b) Give a 95% confidence interval for the mean of the population from which the sample is drawn.
c) Are you quite sure that the average weight of the population of runners is less than 65 kg?

Answer 2

ok first you need to find xbar

Answer 3

oh wait, we can do that in part b) later

Answer 4

sx = sigma/sqrt(n)

sx = ???

Answer 5

ok.

Answer 6

4.5/sqrtn?

Answer 7

n = 24 in this case

Answer 8

0.91855865354

Answer 9

so that's sx

Answer 10

sx = 0.91855865354

Answer 11

now find xbar

Answer 12

ok!how do i do that

Answer 13

add up all of the given numbers in that list

then divide that sum by 24

Answer 14

Oh ok

Answer 15

I realize it's a lot to add up, so I'll save you time by saying that the 24 numbers add up to 1483

Answer 16

can u? i messed up when i was at the very end:(((

Answer 17

divide 1483 by 24 to get the average xbar

Answer 18

61.7916667

Answer 19

good

Answer 20

xbar = 61.7916667

Answer 21

ok

Answer 22

to sum up, we'll use these values

xbar = 61.7916667
C = 1.96
sx = 0.91855865354

Answer 23

Now compute the lower and upper bounds of the CI

Answer 24

um

Answer 25

remember the formulas?

Answer 26

for L and U

Answer 27

its 61.7916667 plus minus 1.96?

Answer 28

i dont remember the rst

Answer 29

there's a *sx at the end

Answer 30

61.7916667 plus minus 1.96 * 0.91855865354


0.91855865354 is the value of sx

Answer 31

61.7916667 plus 1.96 * 0.91855865354 = 63.5920416609??

Answer 32

and the LL is 59.9912917391?

Answer 33

so that's your upper bound, how about your lower bound

Answer 34

good

Answer 35

therefore your 95% CI is (59.9912917391, 63.5920416609)

Answer 36

ok!

Answer 37

c?

Answer 38

Are you quite sure that the average weight of the population of runners is less than 65 kg?

what do you think about this one?

Answer 39

Um.....

Answer 40

im not sure :p

Answer 41

the 95% CI is (59.9912917391, 63.5920416609)

Answer 42

that means that if we generate 100 confidence intervals, then 95 of them will have the population mean mu in it somewhere

Answer 43

so there's a 95% chance (so to speak) that the population mean is in the interval (59.9912917391, 63.5920416609)

Answer 44

okok

Answer 45

so what do you think about c now?

Answer 46

Is it no?

Answer 47

well basically, there's a good chance that the average weight will be in the interval (59.9912917391, 63.5920416609)

Answer 48

since 65 isn't in that interval, that means that the average weight is definitely below 65

Answer 49

ok.

Answer 50

so what should i put for c?

Answer 51

I would say that I'm quite sure because we're 95% confident that the average weight is in (59.9912917391, 63.5920416609), which is less than 65 kg

Answer 52

ok thx! theres one more