In class we’ve talked about confidence intervals and significance tests being two sides of the same coin.The goal of this assignment is to better understand this relationship by:
vFinding confidence intervals by hand
vCompleting significance tests by hand
vUsing StatCrunch to find confidence intervals and run significance tests
vInterpretingand comparing the results ofsignificance tests and confidence intervals
1.For this question we will revisit the example of the 2010 gubernatorial race in California that was discussed in class and that you worked on in HW3.In this race, the exit poll on which TV networks relied for their projections on election night found that, after sampling 3,889 voters, 53.1% said they voted for Democrat Jerry Brown over Republican Meg Whitman.
a.(6pts)By hand, find a 95% confidence interval for the proportion of the population who voted for Brown.Show all of your work, and clearly state:
üYour value of
üYour value ofz
üThe standard error (rounded to 3 decimal places)
üThe confidence interval
b.(3pts)Using StatCrunch, find a 95% confidence interval for the proportion of the population who voted for Brown.
üInsert an image of the output.
c.(10pts)By hand,conduct a significance test to see if there is evidence to support the research hypothesis that the proportion of the population who voted for Brown is greater than 50%.
üShow all five parts of the significance test
üShow all of your calculations.
üInclude an image of the calculator results from StatCrunch in step 4, finding theP-value.
d.(3pts)Using StatCrunch, conduct a significance test to see if there is evidence to support the research hypothesis that the proportion of the population who voted for Brown is greater than 50%.
üInsert an image of the output.
e.(4pts)The media used the results of this exit poll to predict a win for Brown.Based on what you’ve seen in this exercise, answer the questions:
-If only half the population voted for Brown; would it then be surprising that 53.1% of the sampled individuals voted for him?
- Does it make sense that the race was called for Brown?
üExplain your thoughts usingat least 3 sentences.
2.In HW3, you also investigated the 2014 gubernatorial election in Florida, where, in an exit poll of 2696 voters, 50.5% said they voted for Rick Scott and 49.5% said they voted for Charlie Crist.
a.(6pts)By hand, find a 95% confidence interval for the proportion of the population who voted for Scott.Show all of your work, and clearly state:
üYour value of
üYour value ofz
üThe standard error (rounded to 4 decimal places)
üThe confidence interval
b.(3pts)Using StatCrunch, find a 95% confidence interval for the proportion of the population who voted for Scott.
üInsert an image of the output.
c.(10pts)By hand,conduct a significance test to see if there is evidence to support the research hypothesis that the proportion of the population who voted for Scott is greater than 50%.
üShow all five parts of the significance test
üShow all of your calculations.
üInclude an image of the calculator results from StatCrunch in step 4, finding theP-value.
d.(3pts)Using StatCrunch, conduct a significance test to see if there is evidence to support the research hypothesis that the proportion of the population who voted for Scott is greater than 50%.
üInsert an image of the output.
e.(4pts)The media would have used the results of this exit poll to decide if they could predict a win for Scott.Based on what you’ve seen in this exercise, answer the questions:
- If only half the population voted for Scott; would it then be surprising that 50.5% of the sampled individuals voted for him?
- Should the race have been called for Scott based on this exit poll?
üExplain your thoughts usingat least 3 sentences.
3.For this question you will need your GSS data.There are instructions for finding a confidence intervalwith dataand conducting a significance testwith datain the “Working with StatCrunch” file posted in Teams.
a.(4pts)In StatCrunch, find a 99% confidence interval for the mean for the variable “Ideal number of children”.
üInsert an image of the output
üInterpret the output.
b.(6pts)In StatCrunch, run a significance test for the mean for this same variable, letting2, 2.5, and then 3, in each case selecting “” in the alternative hypothesis.
üInsert images of thethreedifferent output windows
üInterpret theP-value in each case.
c.(3pts)In this setting, does the confidence interval approach or the significance test approach seemmore useful in predicting the population parameter?
üExplain your thoughts usingat least 3 sentences.