Question

4. Sarah’s political campaign wants to assess how she will do in the upcoming election. They take a simple random sample of likely voters and ask them who they intend to vote for. The proportion of respondents who say they intend to vote for Sarah is .51 and the margin of error for a 95% confidence interval is .02. Use this information to answer the following questions.

a. Based on this sample, what is the campaign’s best guess about the population proportion of likely voters who intend on voting for Sarah?

b. Based on this sample, create the 95% confidence interval for the population proportion of likely voters who intend on voting for Sarah

c. Assume Sarah needs more than 50% of the vote to win the election. Should her campaign be confident that she will win the election? Explain.

d. Would a 99% confidence interval based on the same sample involve a larger or smaller margin of error? Explain.

Answer 1

a) The campaign’s best guess about the population proportion of likely voters who intend on voting for Sarah is equal the sample proportion which is equal to 0.51. Therefore 0.51 is the required best estimate for the population proportion here.

b) The 95% confidence interval here is obtained as:

This is the required 95% confidence interval here.

c) As the whole confidence interval is not above 0.5 marks, therefore at 95% confidence interval we cannot be sure that Sarah is goind to win the elections.

d) More the confidence level, greater is the critical z value, therefore more would be the margin of error and hence wider would be the 99% confidence interval. 99% confidence interval based on the same sample involve a larger or smaller margin of error. Therefore, 99% confidence interval based on the same sample involve a larger margin of error