Download math-111 test 3 answers spring 2010

MATH-111 DUPRE' TEST 3 ANSWERS (S2010)
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LAB DAY_____________DATE: 21 APRIL 2010
ANSWERS MUST BE CORRECT TO THREE SIGNIFICANT DIGITS
Suppose the population of raccoons in the Okefenokee Swamp has normally
distributed weight with standard deviation UNKNOWN, and Albert the Alligator has a
sample of size 12 raccoons with mean 18 pounds and standard deviation 4 pounds.
1.
Pogo possum uses Albert’s data to make a 95 percent confidence interval for true
mean weight of Okefenokee raccoons. What is the MARGIN OF ERROR of Pogo’s 95
percent confidence interval for the true population mean weight of Okefenokee raccoons
based on Albert’s data?
Use the TInterval and set sample mean =zero. From the readout ME=2.5415.
2.
What is the P-value or significance for Pogo of Albert’s data as evidence that the true
mean weight of the population of Okefenokee raccoons is under 20 pounds?
Use the TTest. P-value=.0555864705 or .0556
3.
At the .05 level of significance should Pogo think Albert’s data establishes that the true
mean weight of this population of raccoons is under 20 pounds? CIRCLE YOUR ANSWER
BELOW.
YES
circle: (NO) because P-value > .05
4.
Howland Owl knows that in fact the true population standard deviation in weight of
Okefenokee raccoons is exactly 4 pounds. What would be the MARGIN OF ERROR of the
95 percent confidence interval for true mean Okefenokee raccoon weight that Howland would
compute using his knowledge of the population standard deviation and Albert’s data?
Use ZInterval and set sample mean=zero. From readout ME=2.2632.
5.
What would Howland think (knowing the true population standard deviation in
Okefenokee raccoon weight is 4 pounds) is the P-value or significance of Albert’s data as
evidence that the true mean weight of Okefenokee raccoons is under 20 pounds.
Use the ZTest. P-value=.0416322192 or .0416
6.
At the .05 level of significance, and knowing the population standard deviation of
Okefenokee raccoons is exactly 4 pounds, should Howland think Albert’s data establishes
that the true mean weight of Okefenokee raccoons is under 20 pounds? CIRCLE YOUR
ANSWER BELOW.
Circle: (YES) because P-value < .05
NO
7.
Suppose that Joe and Sam are each working confidence intervals for a true population
mean and that Joe’s sample size is larger than Sam’s, but in fact they both have the same
sample mean and the same sample standard deviation. Whose margin of error will be larger?
CIRCLE ANSWER BELOW:
JOE’S
Circle: (SAM’S)
8.
Joe is going to make a confidence interval for the true mean breaking strength of
Acme 1000 pound test rope. He knows that the population standard deviation for this rope is
50 pounds. He wants the margin of error to be at most 10 pounds. He also wants to have 99
percent confidence in his margin of error. What is the smallest his sample size can be and
still fulfill all these requirements?
n>([50/10]*invNorm(.995,0,10))2=165.872415, so smallest sample size is n=166.
9.
Howland Owl is planning to take a poll to find out the true percentage of Okefenokee
raccoons who favor him for President of the Okefenokee Swamp in the upcoming election.
He wants to be 95 percent sure of his confidence interval for this true percentage and he
wants the margin of error to be no more than 3 percentage points. What is the smallest
sample size he can use and still fulfill these requirements?
n>([.5/.03]*invNorm(.975,0,1))2=1067.071896, so smallest sample size is n=1068.
We are going to run a hypothesis test to see if our sample data proves that the true mean
breaking strength of Acme 1000 pound test rope is MORE THAN 1200 pounds. We have a
sample having mean breaking strength 1234. In fact the P-value of our data is .04.
10.
What is the P-value of this same data as evidence that the true mean breaking strength
of Acme 1000 pound test rope is NOT EQUAL to 1200 pounds?
P-value=2*(.04)=.08
11.
At the .05 level of significance can we conclude that Acme 1000 pound test rope has
true mean breaking strength NOT EQUAL to 1200 pounds?
CIRCLE YOUR CHOICE:
YES
Circle: (NO)
12.
What about concluding the mean is MORE THAN 1200 pounds at the .05 level of
significance?
The data does allow you to conclude that the mean breaking strength of the rope is more than
1200 pounds since .04 <.05. You should be aware of how this seems to violate logic-we can
prove the mean is more than 1200 but cannot prove it is not equal to 1200.