Question

Question 10: 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).

Question 5: A proposal to amalgamate the two towns of Smallville and Palookatown into one municipality is scheduled to be put to a referendum vote at the next local election. A random survey of 200 voters in each town is conducted, with 113 voters in Smallville indicating their support for the proposal, and 90 voters in Palookatown indicating their support.

a) Calculate confidence intervals for the difference between the levels of support for amalgamation in the two towns, for: i. LOC = 95% ii. LOC = 99%

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.

Answer 1

Question 10

a) For Town Smallville:

= 200, = 113, =113/ 200 = 0.565

For Town Palookatown:

= 200, = 90, = 90/ 200 = 0.45

The value of the pooled proportion is computed, =

Null and Alternative Hypotheses

Critical value:

At =0.05, and the critical value for a two-tailed test is z_c = 1.96

Test Statistics:

Decision about the null hypothesis

Since it is observed that z = 2.3 > z_c = 1.96, it is then concluded that the null hypothesis is rejected.

Conclusion:

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to support the claim that level of support is different in the two towns, at the 0.05 significance level.

b) Using the P-value approach:

p-value is p = 0.0214

Using the p-value method the decision from Part (a) would change for = 0.01, 0.005, 0.001

c) No the level of support for amalgamation is not equal in the two towns. As we know that the sampling is done in an random and unbiased manner. so we can say that there was difference in support for amalgamation in the towns.