Question

Confidence interval

Alice wants to compare whether the price on a birthday cake in two supermarkets differs significantly. She wrote down the daily prices for the last few days and found the difference between the sample means to be $4.01. If the standard deviation of the difference between sample means is $5.46, what is the 95% confidence interval of the sample mean difference?

a between -8.02 and +8.02

b between -10.92 and +10.92

c between -12.03 and +12.03

d between -16.38 and +16.38 @amistre64 @rational @AnswerMyQuestions

Answer 1

what is the z score related to the 95%?

Answer 2

5.46

Answer 3

Okay I think I got it. D?

Answer 4

95% relates to ... well we have 5% in the tails split evenly left and right

a zscore of .95+.05/2 = .975 for the right tail value
or
a zscore of .05/2 = .025 for the left tail value

then its just the setup: CI := mean +- z(sd)

Answer 5

a z of 1.96

so 4.01 + 1.96(5.46) is the upper bound

Answer 6

but thats not an answer choice so im prolly not reading the 'standard deviation of the sample means' part correctly

Answer 7

or, ive forgottenhow to do some basic stuff lol

Answer 8

Maybe we are setting up the formula wrong because I'm not getting the right answers either.

Answer 9

Is a Z score the same as a confidence interval?

Answer 10

the formula for a confidence interval is pretty simple :)

mean, plus or minus, the spread associated with the %

5/2 - 2.5 and a zscore of 1.96 gives us .025 of the area in a tail

Answer 11

maybe they assumed an empirical rule? 2 sds fro the mean are about 95% of the data

Answer 12

careful reading, maybe we are missing something or maybe its just a bad question

Alice wants to compare whether the price on a birthday cake in two supermarkets differs significantly.

2 super markets eh ...



She wrote down the daily prices for the last few days and
found the difference between the sample means to be $4.01.

ok, so the difference if the samples is 4.01


If the standard deviation of the difference between sample means is $5.46

and the sample deviation is this ... no sample sizes are given


what is the 95% confidence interval of the sample mean difference?

Answer 13

all the options are centered around the difference of the means being 0 ....

Answer 14

Sorry I'm confused.

Answer 15

quite frankly the question is messed up

the options dont match the question at all. not a little off; but completly off.

Answer 16

(difference of means) +- z(standard deviation of the means)

this is the formula to use,

if the difference of the means is 0, then we would expect a confidence interval of:

-a to a to represent it. which is what all the options are suggesting.

Answer 17

but 4.01 is NOT equal to 0 so none of the options are valid

unless they are asking for the spread itself: z(sd) which is called the margin of error

Answer 18

4.01 +- 10.71

10.71 isnt in the options

Answer 19

2(sd) = 10.92 IS one of the options

Answer 20

so, my best educated guess is:

they want the margin of error related to the confidence interval of 95%:

mean +- (margin of error) = CI

and instead of using the actual value associated with .025 (z=1.96); they have opted to use the approximation according to the empirical rule: 95% of the data is within 2sds from the mean.

+- 2(sd) is what they seem to want.

the question is bad is all there is to say about it.

Answer 21

Well nothing else is making sense. lol

Answer 22

:) lets go with 10.92 and then go punch kittens ...

Answer 23

Well thanks for the help.