Unformatted text preview: othesis H0:
Alternate Hypothesis H1:
Significance Level α = Population Proportion = 0.56
Population Proportion "not equal" 0.56 5% The name of the TI83/84 calculator function you will be using: 1PropZTest Are the conditions met in order to use this statistical method? Show how you
verified this: Yes. We have a random sample from a huge population, and our sample size is large
enough to pass this test: np(1p) = (300)(0.56)(1  0.56) = 73.92 > 10; So our
Sampling Distribution for the sample proportion should be approximately normal.
From your calculator’s output give the following:
Test Statistic z = 1.40 Interpret what this value is telling you: Our Test Statistic is 1.40 Standard Errors above the hypothesized population
proportion of 56%.
PValue = 16.28% Interpret what this value is telling you: There is a 16.28% probability of getting a Test Statistic this far away (or farther away)
from the hypothesized population proportion of 56% IF the Null Hypothesis is true. Which one is your conclusion (Click in the box next to your choice):
Failed to Reject H0
Reject H0 and Accept H1
Show the reason for your conclusion (to prove you weren’t just guessing): Pvalue > Significance Level
16.28% > 5%, so the probability is not small enough to be considered unusual.
Which one is your conclusion “in context” (Click in the box next to your choice):
“There is not sufficient evidence at the 0.05 significance level to support the
claim that this population proportion has changed from its 1999 level.
“There is sufficient evidence at the 0.05 significance level to support the
claim that this population proportion has changed from its 1999 level.
Page 8 of 9 b) If you are wrong about this conclusion, what type of error would it be? Type II Error. This would mean that the population proportion of all cases of tuberculosis
that are from foreignborn residents is different from 56%, but we didn't catch it. This is a
Missed Opportunity.
c) Find a 95% confidence interval for the proportion of all cases of tuberculosis
that are from foreignborn residents.
The name of the TI83/84 calculator function you will be using: 1PropZInt State your answer in words: We are 95% confident that the population proportion of ALL cases of tuberculosis that
are from foreignborn residents is between 54.456% and 65.544%.
Notice that the hypothesized population proportion of 56% is in this interval, which is
why it was not rejected in the Hypothesis Test.
d) How large of a sample size would you need in order to have a 95% confidence
level and a margin of error E = .025? Use your prior estimate for p: ˆp=x/n .
Be sure to show how your answer was calculated: n = (phat) (1  phat) (z / E)^2 = (0.6) (1  0.6) (1.9600 / 0.025)^2 = 1475.1744
We Round UP to: n = 1476 ================================= The End
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 Winter '08
 DR.KIM
 Statistics, Statistical hypothesis testing, significance level

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