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wrote...
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2 weeks ago
A statistics professor asked her students whether or not they were registered to vote. In a sample of 50 of her students (randomly sampled from her 700 students), 35 said they were registered to vote.

Find a 95% confidence interval for the true proportion of the professor's students who were registered to vote. (Make sure to check any necessary conditions and to state a conclusion in the context of the problem.)
Textbook 

Stats: Modeling the World


Edition: 4th
Authors:
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wrote...
Posts: 267
2 weeks ago
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We have a random sample of less than 10% of the professor's students, with 35 expected successes (registered) and 15 expected failures (not registered), both of which are at least ten, so a Normal model applies.
n = 50, = = 0.70, = 1 - = 0.30, so SE() = = = 0.065
Our 95% confidence interval is:
  ± z*SE() = 0.70 ± 1.96(0.065) = 0.70 ± 0.127 = 0.573 to 0.827

We are 95% confident that between 57.3% and 82.7% of the professor's students are registered to vote.

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wrote...
2 weeks ago
Smart ... Thanks!
zar
wrote...
2 weeks ago
A statistics professor asked her students whether or not they were registered to vote. In a sample of 50 of her students (randomly sampled from her 700 students), 35 said they were registered to vote.

Explain what 95% confidence means in this context.
wrote...
2 weeks ago
If many random samples were taken, 95% of the confidence intervals produced would contain the actual percentage of the professor's students who are registered to vote.
wrote...
2 weeks ago
A statistics professor asked her students whether or not they were registered to vote. In a sample of 50 of her students (randomly sampled from her 700 students), 35 said they were registered to vote.

What is the probability that the true proportion of the professor's students who were registered to vote is in your confidence interval?
wrote...
2 weeks ago
There is no probability involved-once the interval is constructed, the true proportion of the professor's students who were registered to vote is in the interval or it is not.
wrote...
2 weeks ago
This calls for a celebration Person Raising Both Hands in Celebration
wrote...
2 weeks ago
A statistics professor asked her students whether or not they were registered to vote. In a sample of 50 of her students (randomly sampled from her 700 students), 35 said they were registered to vote.

According to a September 2004 Gallup poll, about 73% of 18- to 29-year-olds said that they were registered to vote. Does the 73% figure from Gallup seem reasonable for the professor's class? Explain.
wrote...
2 weeks ago
The 73% figure from Gallup seems reasonable since 73% lies in our confidence interval.
wrote...
2 weeks ago
A statistics professor asked her students whether or not they were registered to vote. In a sample of 50 of her students (randomly sampled from her 700 students), 35 said they were registered to vote.

If the professor only knew the information from the September 2004 Gallup poll and wanted to estimate the percentage of her students who were registered to vote to within ±4% with 95% confidence, how many students should she sample?
wrote...
2 weeks ago
ME = z*
0.04 = 1.96
n =   = 473.24 ≈ 474
Note: Since there are only 700 students in the professor's class, she cannot sample this many students without violating the 10% condition!
wrote...
2 weeks ago
I appreciate what you did here, answered it correctly Smiling Face with Open Mouth
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