I believe that the homeless population in Manchester, NH is .20 of the total Manchester, NH population. I asked 300 random people in Manchester, NH if they knew at least one homeless person and 67 out of the 300 people I asked knew at least 1 homeless person. Test this hypothesis at the .05 significance level.

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.CT: Chapter Test
Problem 24CT: Show the sample space of the experiment: toss a fair coin three times.
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I believe that the homeless population in Manchester, NH is .20 of the total Manchester, NH population. I asked 300 random people in Manchester, NH if they knew at least one homeless person and 67 out of the 300 people I asked knew at least 1 homeless person. Test this hypothesis at the .05 significance level. 

Expert Solution
Step 1

Given Information:

Hypothesized value (p0) = 0.20

Sample size (n) = 300

Out of which X = 67 people knew at least 1 homeless person.

Significance level α=0.05

 

Sample proportion is obtained using the formula:

p^=Xn    (X is the number of successes)=67300=0.22333333330.22333

 

State the Hypothesis as follows:

Null HypothesisH0:p=0.20

Alternative HypothesisHa:p0.20

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