Question

statistics and probability questions, solve clearly, show steps and in 30 minutes for thumbs up vote

please answer all parts of the question, garunteed thumbs up.

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) Find the proportion of voters in support of amalgamation for both towns.
b) Calculate confidence intervals for the difference between the levels of support for amalgamation in the two towns, for:
i. LOC = 95%
ii. LOC = 99%
c) Comment on whether or not the results from Part (a) support the idea that one town is more supportive, overall, of the amalgamation proposal.
d) 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.
e) Use the p-value method to determine if your decision from Part (d) above would change for any of
α = 0.10, 0.01, 0.005, 0.001 .
f) 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).

Answer 1

Dear student we can provide you with the solution of 4 sub question at a time.

a) the proportion of voters in support of amalgamation for Smallville =

the proportion of voters in support of amalgamation for Palookatown =

b) We have to calculate the confidence interval for the difference between proportion

i) We will calculate the 95% confidence interval for the difference here

ii)

We will calculate the 99% confidence interval for the difference here

c) The results from part (a) do gives a hint that one town is more supportive, overall, of the amalgamation proposal, since there is a difference in the point estimate of the proportion calculated in (a).

but constructive conclusion can be made using the results of (b)

d)

e) Using the P-value approach: The p-value is p = 0.0214, and since p = 0.0214 <0.05, it is concluded that the null hypothesis is rejected.

the result will change for significance level 0.01 and 0.001.

For them we will fail to reject the null hypothesis as the P value will be greater than the significance level.