Question

National Fuelsaver Corporation manufactures the Platinum Gasaver, a device they claim "may increase gas mileage by 22%." Here are the percent changes in gas mileage for 15 identical vehicles, as presented in one of the company's advertisements:

48.3 46.9 46.8 44.6 40.2 38.5 34.6 33.7
28.7 28.7 24.8 10.8 10.4 6.9 -12.4

Would you recommend use of a t confidence interval to estimate the mean fuel savings in the population of all such vehicles? Explain your answer.

Answer 1

@amistre64

Answer 2

there is usually a table defining a path to take that ends up in z, t, or bootstrapping

Answer 3

how do i find that?

Answer 4

um, its in all the textbooks

Answer 5

..

Answer 6

im looking in my textbook :) i believe if memory serves that if n<30 we go t

Answer 7

Ok!

Answer 8

the one i was thinking of had to do with:

if sigma unknown, and data is normally distributed, use t statistic in place of z stats

Answer 9

ok

Answer 10

Would you recommend use of a t confidence interval to estimate the mean fuel savings in the population of all such vehicles? Explain your answer.

Answer 11

my idea at the moment, maybe we should determine if the data presented is normally distributed or not

Answer 12

Ok, how would i do that

Answer 13

a stem and leaf is a simple way to see if it is; the outline of the leafs will mimic a histogram

Answer 14

can u show?

Answer 15

you were already shown this process way back in other chapters .....

Answer 16

cut off the first digit and stack the rest in rows or columns

Answer 17

i never learned

Answer 18

48.3 46.9 46.8 44.6 40.2 38.5 34.6 33.7
28.7 28.7 24.8 10.8 10.4 6.9 -12.4
these are the numbers so

Answer 19

spose we have a set of number 23 25 27 23 29 21, the stem is the 20 parts, and the leafs are the ones

2 | 1 3 3 5 7 9

Answer 20

Oh ya i know how to do that

Answer 21

what do i do with the negative value tho ? the -12.4

Answer 22

place it on the other side of a 0 :)

Answer 23

-1|
0|
1|
2|
3|
4|
5|

Answer 24

-1| 2
0|
1|
2| 4.8
3|
4|
5|

Answer 25

you can make columns instead .. but thats difficult to format up on here

Answer 26

on the right track?^

Answer 27

thats on the right track yes :) but -1|2.4

Answer 28

for simplicity, the numbers dont really have to be in order ... just stacked in the right row is all

Answer 29

oh ok

Answer 30

its the shape that we are after

Answer 31

..and if anyone else looking in here has a better solution to this post, feel free to chime in :)

Answer 32

-1| 2.4
0|
1| 0.4 0.8
2| 4.8 8.7
3| 3.7 4.6 8.5
4| 0.2 6.4 6.8 6.9 8.3
5|
6| .9

Answer 33

is that right.. it hard to do here

Answer 34

that 6.9 should be seen as 06.9 since we are cutting off the ten spots

Answer 35

ok how should the end table look ?

Answer 36

-1| 2.4
0| 6.9
1| 0.4 0.8
2| 4.8 8.7 8.7
3| 3.7 4.6 8.5
4| 0.2 6.8 6.9 8.3 4.6

thats seems about right

Answer 37

ok cool thx

Answer 38

from the looks of this data, its skewed, and not normally distributed

Answer 39

So that ould be my answer?^

Answer 40

--> The data appears to be skewed, and NOT normally distributed.

Answer 41

correct, and im trying to recall if the t statistic is related to the population, or the sample distribution at the moment

Answer 42

thx!

Answer 43

i have one more prob im posting now, can u look ?:P

Answer 44

i found the chart in my book :)

is sigma known? No.
Is the pop normally distibuted? If yes, t stat
If no, check n size
dunno? id conservatively go with no
is n>30? no
use nonparametric of boot strapping methods then

Answer 45

that would personally be my "reasoning"