Question

A bottling plant produces one-liter bottles of soda. The actual distribution of volumes of soda dispensed to bottles is Normal, with mean μ and standard deviation σ = 0.05 liter. We randomly select six bottles and measure the volume of soda in each. The results of these six measurements (all in liter units) are
1.05 1.04 1.01 1.06 0.94 0.99

Answer 1

Based on these data, a 90% confidence interval for μ is
A. 0.917 liters to 1.113 liters.
B. 0.933 liters to 1.097 liters.
C. 0.975 liters to 1.055 liters.
D. 0.981 liters to 1.049 liters.


Which of the following is true?
A. In taking very many random samples of six bottle volumes, each time computing a 90% confidence interval for the average volume, 90% of confidence intervals will capture μ.
B. There's a .90 probability that μ is contained in the interval computed in problem 2, above.
C. If we construct 10 confidence intervals for m, each based on a random sample of six bottle volumes, exactly nine of them will capture μ.
D. All of the above.

Answer 2

@jim_thompson5910

Answer 3

now I remember for the first one we used that one formula with sqrt(n) k and something else...?

Answer 4

90% seems like it would be D

Answer 5

yeah i agree with A and C, which automatically means it has to be D

I think A is a much better way to do it because only doing 10 CI's is a bit silly

Answer 6

100 would be much better

Answer 7

Sorry jus tgot out of the shower... A and C? It cannot be A or B because that's outside the ranges. C is a bit longer imo.

Answer 8

Idk about #2 lets take a look.

Answer 9

I think that part 2 also might be D, but not too sure... @jim_thompson5910

Answer 10

or B because B is the obvious choice that I can see.

Answer 11

I'm not sure what Capture mu means.....

Answer 12

i think choices A-C all say the same thing (pretty much), which why I'm thinking it's D

Answer 13

Capture mu = mu is in the interval

Answer 14

ah...

Answer 15

yeah A and C seem like the same thing...

Answer 16

If we construct 10 confidence intervals for m, each based on a random sample of six bottle volumes, exactly nine of them will capture μ.

Answer 17

wouldn't that be false, shouldn't they all be within mu?

Answer 18

you mean mu within the interval?

Answer 19

yeah I meant 1 SD of mu :P

Answer 20

I had to look up at what mu was again :P

Answer 21

when they say "capture mu" they mean that the confidence interval contains mu

Answer 22

ie mu is somewhere in the confidence interval

Answer 23

Ic...

Answer 24

I would think it's always in the interval?

Answer 25

no way, mu is not always in the inveral

if we knew that for sure, then why need stats?

Answer 26

interval*

Answer 27

>(?

Answer 28

Idk it seems from #1 that when it says "the interval is." this to this, but mu was in it.

Answer 29

but it seems like we dont'; know what MU is.

Answer 30

sure mu is in that interval, but any CI in general, not always

Answer 31

Hmm... Messed up man LOL....

Answer 32

oh wait, i'm thinking xbar....we don't even know mu lol

Answer 33

I hatw stats SOO MUCH.

Answer 34

yeah we don't know mu.

Answer 35

But by basing off of those 6 choices, we can take an average/mean as well....

Answer 36

but those values represent a population, which we have no clue about

Answer 37

true story.. :P. MEH

Answer 38

@jim_thompson5910 apparently D wasn't the right answer :P.

Answer 39

what was it?

Answer 40

Prob B :P.

Answer 41

probably A huh? oh they didn't tell you?

Answer 42

They didn't give me the right answer >(.

Answer 43

i see

Answer 44

Stupid tho.... I guess in case people CHEAT. :P

Answer 45

A sounds like the best answer, but C is kinda similar

Answer 46

true

Answer 47

I mean really who cheats? :P

Answer 48

Yeah that's why I assumed B.....

Answer 49

a lot of people i guess, idk

Answer 50

Open Study is for learning ! :P.