Question

Is there sufficient evidence to conclude....

Answer 1

Fish are unsafe to eat is there PCB exceeds over 5 PPB. A random sample of 10 fish taken from a local lake resulted in the concentrations below
2.6, 6.6, 4.8, 5.4, 5.1, 4.5, 6.9, 4.9, 3.7, 3.8

is there sufficient evidence to conclude that the mean PCB exceeds 5 ppb?
use alpha = .05

Answer 2

how far did you get?

Answer 3

Honestly not sure how to work around this one!
I know I need to start off with a HO and an Ha
which i would say is HO = 4.83 HA > 4.83

Answer 4

where are you getting 4.83 ?

Answer 5

oh that's xbar

Answer 6

no, the hypothesis test for the mean always has mu in the hypothesis

Answer 7

Ho: mu = ???
Ha: mu > ???

Answer 8

we don't need to test xbar because we know exactly what it is...4.83

we don't know much about the population, which is why we're conducting the test on the population mean mu

Answer 9

oh, so basically we cant write a hypothesis bc we cant calculate the mu?

Answer 10

no, we write the hypothesis based on mu

Answer 11

so what are the hypotheses?

Answer 12

ho: 5=mu
hu: 5 > mu
? Sorry if this is wrong i just never get stats haha

Answer 13

you sorta have the right idea

Answer 14

it's just mixed up

Answer 15

the variable should be on the left side

Answer 16

Ho: mu = 5
Ha: mu > 5

Answer 17

so the status quo is that the mean is 5

the alternative challenge is the mean is more than 5

Answer 18

okay! getting it .. slowly

Answer 19

what kind of test is this? one tailed? or two tailed?

Answer 20

one tailed?

Answer 21

to the left? or to the right?

Answer 22

to the right? bc we want to see if it exceeds 5?

Answer 23

correct

Answer 24

so the p value will be found by finding the area to the right of the test statistic

Answer 25

we'll need that next, so what is the test statistic

Answer 26

okay so test statistic would be (4.83-5)/(1.30/3.26)
-.17/.40 = -.425

Answer 27

I'm getting

t = (xbar - mu)/(s/sqrt(n))

t = (4.83 - 5)/(1.301324112/sqrt(10))

t = -0.41310784705466

Answer 28

Looks like we used the same #'s just rounded the S differently

Answer 29

yeah

Answer 30

btw, sqrt(10) = 3.16 roughly not 3.26

Answer 31

anyways, I'd use the longer decimal expansions and don't round until you get to the final answer

Answer 32

Okay thats fine. so ill keep -0.41310 for the test stat.

Answer 33

t = -0.4131 works, yeah

Answer 34

now find the area to the right of t = -0.4131 to calculate the p value

Answer 35

16.92? I looked at df=9 and .05 on a p value table

Answer 36

look in the row df = 9

Answer 37

between which two columns is 0.413 located?

Answer 38

try this table

http://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf

Answer 39

between .50 and .25
the # are 0.000 & 0.703

Answer 40

so that means the area to the right of 0.413 is between 0.5 and 0.25

by symmetry, the area to the left of -0.413 is between 0.5 and 0.25

so the area to the right of -0.413 is between between 0.5 and 0.75 (I subtracted 0.5 from 1 to get 0.5 and I subtracted 0.25 from 1 to get 0.75)

Answer 41

it turns out that the area to the right of -0.413 is 0.6554018441

but we don't need the actual p value

Answer 42

if we know the p value is between 0.5 and 0.75, then what can we say about the null hypothesis?

Answer 43

alpha = .05

Answer 44

we fail to reject! bc the p is greater than alpha

Answer 45

much much greater (than even the largest significance level usually used, alpha = 0.10)

Answer 46

you have the correct decision

Answer 47

so what does that mean? how do we interpret failing to reject the null?

Answer 48

Yes there is sufficient evidence that says pcb exceeds 5

Answer 49

go back to the null and alternative hypothesis you set up

Answer 50

we are failing to reject Ho (since the p value is larger than alpha)

Answer 51

okay so we fail to reject ho, which means it is true. so mu does equal 5. so it does not exceed 5, there is not enough sig. evidence

Answer 52

it doesn't necessarily mean the null is true

we just don't have enough statistical evidence to disprove and say it's false

Answer 53

so yes, there is not a sufficient amount of evidence to conclude that the mean PCB exceeds 5 ppb

Answer 54

Okay. Thank so much for having patience - you really made this clear!!

Answer 55

I'm glad I have

Answer 56

Yup - thanks again! 1 last question in this death trap of a hw.. haha