Question

A political poll estimates that 48% of Democrat voters will vote for Elizabeth Warren in the presidential primaries. They provide a "margin of error" of 3 percentage points, which leads to a 95% confidence interval of 45% to 51%. a) Explain what a 95% confidence level means. b) why is a confidence interval needed here? What does it tell us that the "48%" does not tell us? c) Which of the following is the best interpretation of the confidence interval? i) 95% of the samples had between 45% and 51% of respondents supporting Warren. ii) There's a 95% chance that between 45% and 51% of those sampled support Warren. iii) We are 95% confident that between 45% And 51% of all voters support Warren. iv) We are 95% confident that between 45% and 51% of those sampled support Warren. 3. Educators introduce a new math curriculum and measure 45 students' scores before and at the end of the academic year using an exam widely believed to accurately measure students understanding. The average score at the start the year was 65%, and after was 75%. a) In words, what are the null and alternative hypothesis tests that the educators would most likely be interested in testing? b) What does a hypothesis test tell us that we can't learn from simply noting that students improved 10 percentage points? c) Suppose the p-value from this hypothesis test was 0.54. Explain how to interpret this value in this context.

Answer 1

Please see attachment

Explanation:

Please see attachment

Answer 2

Explanation:

The confidence level tells us how sure we can be. It is expressed as a percentage and represents how often the true percentage of the population who would pick an answer lies within the confidence interval. The 95% confidence level means you can be 95% certain.

b) The confidence interval is needed to estimate the percentage of democrats voters that will vote for Elizabeth Warren in the presidential primaries. 48% tells us the percentage of democrats voters that will vote for Elizabeth Warren in the presidential primaries of a given sample not for the all voters.

c) We are 95% confident that between 45% and 51% of all voters support women.