33 d what would happen to the width of your interval

33
(d) What would happen to the width of your interval if you were to construct a 99% CI instead
(using the same survey results)?
(e) Interpret the interval you constructed in part (c).
(f) Explain what the corresponding confidence level means.
(g) What (minimum) sample size would be needed for a 95% (conservative) confidence interval with
a margin of error of 0.06 (or 6%)?

Cool-­‐Down: Interpretations of Confidence Intervals
Consider once again the survey of American families, and recall that the 95% (conservative) confidence
interval for the proportion of all such families that ate dinner together is given by (0.56, 0.70).
Below are answers provided by students when asked to now give an interpretation of the actual 95%
confidence interval computed in the study. Assess which are correct and which are not correct
explanations as to what the interval (0.56, 0.70) means (in the context of this study)?
1. There is a 95% chance the confidence interval of (0.56, 0.70) will contain the true population
proportion of all families that ate dinner together last Sunday night.
Correct Not Correct
3. If we repeated this study many times, the true proportion of all families that ate dinner together last
34
Correct Not Correct

35

36
Lab 4: Hypothesis Testing for a Population Proportion
Objective : In this lab, you will learn an important statistical technique that will allow you to answer the
question, “Was our observation due to chance, or is it more significant ?” The objective is to guide you
through the ideas behind tests of statistical significance and the statistical language involved. This lab
first presents a general overview of testing. Then, the In-­‐Lab Project discusses the large sample
Z-­‐test for a population proportion, as well as providing practice in answering the question of whether an
event can be attributed to chance.
Application: Lucy is an Ann Arbor resident who is considering the possibility of running for a seat on the
City Council. To decide if she should invest time and money in her campaign, she wants to conduct some
research to see if there is evidence that she could win the election (i.e. she could receive a majority of all
the votes).
Overview:
Hypothesis Tests: A test of hypotheses (or significance test ) is a procedure designed to assess what the
evidence provided by the data says about some statement about a population parameter. When we
conduct this hypothesis test for Lucy, we are interested in testing if the population proportion of votes
that would be cast for Lucy is greater than 0.5, ensuring her victory.
Hypothesis Testing Steps:
1. Determine appropriate null and alternative hypotheses
and set ∝ .