MATH-111 DUPRE' TEST 3 ANSWERS (S2010)
FIRST NAME______LAST NAME______ANSWERS______
(PRINT IN LARGECAPITALS)(PRINT IN LARGER CAPITALS)
LABDAY______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.
YEScircle:(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 < .05NO
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’SCircle: (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:YESCircle: (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.