Question 9:

Referring to the data from Question 3, comparing tree heights in two different forest areas:

a) Assume that this data was collected after a claim was made that the mean tree heights in these two

forest areas are equal.. Test this claim at LOC = 95%, using the critical value method.

b) Explain how the 95% confidence interval for the difference in mean tree heights from these two forest

areas (as calculated in Question 3(a)) confirms the result from Part (a) of this question above.

c) Use the p-value method to determine if your decision from Part (a) above would change for any of

= 0.10, 0.01, 0.005, 0.001 .

d) Assuming that the samples were truly random, do you think that the average tree heights in these two

forest areas are truly different, or are the differences observed probably just attributable to random

sampling error? Explain in the context of your answers above (Note: there is no single right answer to

this question but your answer needs to be consistent with the arguments supporting it).

Question 10:

Referring to the data from Question 4, comparing the body-mass of people before and after switching

from driving to walking to/from work:

a) Assume that this data was collected after a claim was made that switching from driving to walking does

not lead to a change in weight. Test this claim at LOC = 99%, using the critical value method.

b) Explain how the 99% confidence interval for the average net change in weight (as calculated in

Question 4(a)) confirms the result from Part (a) of this question above.

c) Use the p-value method to determine if your decision from Part (a) above would change for any of

= 0.10, 0.05, 0.005, 0.001 .

d) Assuming that the sampling in this study was done in a random and unbiased manner, do you think

that switching from driving to walking is linked to weight change among this population, or are the

observed weight changes probably just attributable to random sampling error? Explain in the context

of your answers above (Note: there is no single right answer to this question but your answer needs

to be consistent with the arguments supporting it).

Question 11:

Referring to the data from Question 5, comparing the levels of support for an amalgamation proposal in

the two potentially-affected towns:

a) Assume that this data was collected after a claim was made that the level of support is different in the

two towns. Test this claim at LOC = 95%, using the critical value method.

b) Use the p-value method to determine if your decision from Part (a) above would change for any of

= 0.10, 0.01, 0.005, 0.001 .

c) Assuming that the sampling in this study was done in a random and unbiased manner, do you think

that the level of support for amalgamation is equal in the two towns, or are observed differences

probably just attributable to random sampling error? Explain in the context of your answers above

(Note: there is no single right answer to this question but your answer needs to be consistent with the

arguments supporting it

Question3

The table below shows random sample data of tree heights (in m), taken from two separate forest areas. Tree heights in these forests are assumed to follow an approximately normal distribution. Forest Area 1 Forest Area 2 11.6 14.4 8.3 14.9 12.8 21.9 13.3 21.8 12.0 14.4 13.2 13.4 10.1 18.7 12.1 17.7 14.7 23.1 14.0 23.9 11.9 15.2 12.4 18.5 12.5 14.9 11.2 19.0 a) Calculate 90%, 95%, and 99% confidence intervals for the difference between the mean tree heights in these two forest areas. b) Comment on what the results from Part (a) suggest about any claims that might be made suggesting that the average tree heights in these two forests are about the same. Explain your answer in reference to the confidence intervals which you calculated. Question 4: The table below shows (in kg) the body-mass (aka: weight) of a group of study subjects from a town, who were weighed before and then 1 year after switching from driving to walking to and from their work: Subject Weight Before Weight After 1 93 87 2 67 71 3 77 70 4 80 74 5 111 96 6 97 95 7 88 88 8 83 89 9 103 94 10 92 86 a) Assuming that the net change in weight among individuals follows a roughly normal distribution, calculate 90%, 95%, and 99% confidence intervals for the average net change in weight among all people from this town who switch from driving to walking to work. b) What do the results say about whether or not there is compelling evidence that switching modes of commuting leads to weight loss? Explain why or why not the answers to this question are the same, at all LOCs from Part (a). Question 5: A proposal to amalgamate the two towns of Palookatown and Smallville into one municipality is scheduled to be put to a referendum vote at the next local election. A random survey of 100 voters in each town is conducted, with 57 voters in Palookatown indicating their support for the proposal, and 43 voters in Smallville indicating their support. a) Calculate 90% and 95% confidence intervals for the difference between the levels of support for amalgamation between the two towns. b) Comment on whether or not the results from Part (a) support the idea that one town is more supportive, overall, of the amalgamation proposal. c) Redo Part (a) at LOC = 99%. d) Redo Part (b) based on the answer from Part (c).