Question

The following is based on information from The Wolf in the Southwest: The Making of an Endangered Species by David E. Brown (University of Arizona Press). Before 1918, the proportion of female wolves in the general population of all southwestern wolves was about 50%. However, after 1918, southwestern cattle ranchers began a widespread effort to destroy wolves. In a recent sample of 34 wolves, there were only 10 females. One theory is that male wolves tend to return sooner than females to their old territories where their predecessors were exterminated. Do these data indicate that the population proportion of female wolves is now less than 50% in the region? Use a significance level of 0.05
a. (1pt) What is the question and parameter of interest?
b. (2pts) State the null and alternative hypotheses.
c. (2pts) Check the conditions for inference.
d. (2pts) Calculate the test statistic. Show work!
e. (1pts) Give the appropriate p-value and state whether it is one-sided or two-sided.
f. (3pts) Calculate the appropriate 95% confidence interval. Show work!
g. (4pts) Finally, using the results from parts e and f, summarize your conclusions. Interpret the CI and results of your test. Use the four part conclusion method. Include context!

Answer 1

The following is based on information from The Wolf in the Southwest: The Making of an Endangered Species by David E. Brown (University of Arizona Press). Before 1918, the proportion of female wolves in the general population of all southwestern wolves was about 50%. However, after 1918, southwestern cattle ranchers began a widespread effort to destroy wolves. In a recent sample of 34 wolves, there were only 10 females. One theory is that male wolves tend to return sooner than females to their old territories where their predecessors were exterminated. Do these data indicate that the population proportion of female wolves is now less than 50% in the region? Use a significance level of 0.05
a. (1pt) What is the question and parameter of interest?
b. (2pts) State the null and alternative hypotheses.
c. (2pts) Check the conditions for inference.
d. (2pts) Calculate the test statistic. Show work!
e. (1pts) Give the appropriate p-value and state whether it is one-sided or two-sided.
f. (3pts) Calculate the appropriate 95% confidence interval. Show work!
g. (4pts) Finally, using the results from parts e and f, summarize your conclusions. Interpret the CI and results of your test. Use the four part conclusion method. Include context!

Answer 2

@jim_thompson5910

Answer 3

I think I should be able to figure out a, b, c , and d

Answer 4

ok tell me what you get

Answer 5

Let me work on this for a bit and I will tag you

Answer 6

ok

Answer 7

@jim_thompson5910

Answer 8

Okay so the question is out of a pop. of 50 how many wolves are female when returning to a region?

Answer 9

the null: mu = 50
alternative: mu < 50

paramters: interested in population of wolves

was ths ample obtained using a random mech?

-No

Is the pop. normal distributed or n>=30?

-yes

Do we know pop. standard deviation?

-No

Answer 10

paramters would be female wolves

Answer 11

would theory be considered a random mech?

Answer 12

What question are the researchers trying to answer? This is a very specific question stated in the problem.

Answer 13

Do these data indicate that the population proportion of female wolves is now less than 50% in the region?

Answer 14

correct

Answer 15

the parameter is buried in the question

Answer 16

I am thinking...

Answer 17

I need to find a sample praportion?

P^ = 10/34 = 0.29411

Answer 18

what does the sample proportion estimate?

Answer 19

P^ = # success / the pop.

Answer 20

the sample praportion

Answer 21

the sample proportion estimates the sample proportion?

Answer 22

fill in the blank

the sample proportion is approximately equal to the ________

Answer 23

true population portion p

Answer 24

good

Answer 25

if we did a census, we could find the true population proportion p

however, that's way too costly (in terms of time, money, resources, etc) so we use stats and rely on the sample proportion

Answer 26

so the p^ is the sample praportion and we can use the equation to find the true population portion of p? How?

Answer 27

parameter of interest: population proportion of female wolves

statistic of interest: sample proportion of female wolves

the statistic estimates the parameter

Answer 28

so hopefully this wraps up the question `What is the question and parameter of interest?` ?

Answer 29

Does the data indicate that the population proportion of female wolves is now less than 50% in the region? And population proportion of female wolves is our paramter of interest.

p^ = 10/34 = 0.29411

10 being the number of female wolves and 34 being the sample population

Answer 30

`p^ = 10/34 = 0.29411` is the sample proportion

34 is NOT the sample proportion. It helps lead you to it though

34 is the sample size

Answer 31

number of female wolves in sample = 10
number of wolves in sample (male+female) = 34

sample proportion of female wolves = p-hat = 10/34

Answer 32

okay

Answer 33

so about 30%

Answer 34

10/34 = 0.29411764705882

so roughly 0.2941

Answer 35

29.41%

Answer 36

that will come later though and doesn't apply to part (a)

Answer 37

(b) `State the null and alternative hypotheses.`

Answer 38

H_o = 50
H_A < 50

Answer 39

Ho is not equal to 50

Ho is not a number, it's a symbol that stands for "null hypothesis"

it makes no sense to say "the null hypothesis is 50"

Answer 40

use the parameter in part (a)

hopefully you'll notice that the parts build on each other as you go along

Answer 41

The population proportion of female wolves is now less than 50% in the region

Answer 42

This is our claim, the null is what we are referring to a general statement

Answer 43

how can we shorten "population proportion" in terms of symbols?

Answer 44

oh...

Answer 45

P^ = 29.41
P^ < 29.41

Answer 46

but we know the value of p-hat

it's 0.2941

why do we need to conduct a test on the value of p-hat?

Answer 47

btw 0.2941 is not the same as 29.41

Answer 48

tie the parameter (in symbolic form) with the question

Answer 49

sample praportion is a good estimator for the true population proportion P

H_o: P = 0.29411
H_A: P < 0.2941

Answer 50

the ultimate goal is to figure out the population proportion p

the null would be
Ho: p = 0.50
the alternative would be
Ha: p < 0.50

so we assume the null is true, we assume p = 0.50
then we test if that assumption is true or not
if the p value is smaller than alpha, then we reject the null. Otherwise, we fail to reject and "accept" the null

Answer 51

H_o = 50
H_A < 50

my bad this was a mistake. I meant to use a mu

Answer 52

I guess I would have been wrong anways since I didn't use a p

Answer 53

H_o: mu = 50
H_A: mu < 50

Answer 54

`H_o: mu = 50`
`H_A: mu < 50`

no, I just stated the hypotheses

Answer 55

so when dealing with praportion i have to use a symbol p huh? I would get points knocked off if I used mu instead?

Answer 56

proportion

Answer 57

`i have to use a symbol p huh? `

yes for population proportion

Answer 58

Okay I will make a note on my cheat sheet of this. I am on c now.

Answer 59

`I would get points knocked off if I used mu instead?`
yes you would and it's not because it's a trivial mistake. It leads you down the wrong path and wrong test method. So you're likely to get more points taken away for using the wrong test statistic and wrong test method

Answer 60

p and mu aren't just symbols

as all symbols do, they represent something greater and more complex (which is why it's handy to use a convenient letter)

Answer 61

okay. i am looking at c now.

Answer 62

was the sample obtained using a random mechanism?

Answer 63

yes

Answer 64

is the pop normal distributed or n>=30?

Answer 65

this might help

http://apcentral.collegeboard.com/apc/members/repository/ap03_stats_assumption_31840.pdf

Answer 66

yes our n>=30

Answer 67

if you're in an AP stats class then it would be really relevant since it's from CollegeBoard (the people who make the AP curriculum)

Answer 68

no i am in intro to engineering stats

Answer 69

My instructor told us to use the 3 questions:

1. Was the sample obtained using a random mech?

2.Is the population normal distributed or n>=30?

3. Do you know population standard deviation, sigma?

Answer 70

alright

Answer 71

if I didn't have sigma I'd use the t-test , thanks for the link. I will look over it briefly while i study.

Answer 72

it doesn't mention SRS anywhere, but let's hope these researchers used it

Answer 73

I think what you stated is most of the time true in our problems. I have not really asked my instructor about these conditions. Question 2 for example he said it's a rule of thumb your n needs to be 30 or more.

Answer 74

1. Yes
2. Yes
3. No

Answer 75

yeah I think the SRS condition is so automatic that it's hardly mentioned.

Answer 76

I agree with your three answers to those 3 sub-questions

Answer 77

in #2 I would be more specific and say "yes, n >= 30"

Answer 78

Okay

So would you have to calculate SRS in upper level stats courses?

Answer 79

SRS refers to simple random sample

Answer 80

you use a computer most likely (to be quick and efficient with the random process)

Answer 81

don't worry about the nitty gritty, that will come later when you're actually setting up a study

Answer 82

t-test? I need the sample std though

Answer 83

you have a proportion, which means you use a z test

Answer 84

i can't use the z test. i don't know sigma

Answer 85

do i need to use the one sample proportion z confidence interval?

Answer 86

have a read of this page

http://stattrek.com/hypothesis-test/proportion.aspx?Tutorial=AP

notice how on that page it says `Test statistic. The test statistic is a z-score (z) defined by the following equation`

Answer 87

it's a different kind of z test

Answer 88

I'll be right back

Answer 89

i;ve never seen that equation before...