Chapter 9 Hypothesis Testing 9.4 Testing a Hypothesis about a Population Proportion.
Chose Project Type A Testing a hypothesis about a population average.
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Transcript of Chose Project Type A Testing a hypothesis about a population average.
S
Hypothesis Testing: High School
Extracurricular Activities
ByCasey McCurdy
S
Chose Project Type ATesting a hypothesis about a population average
Focus of Study
University of Notre Dame students are known to typically have been very involved in high school, so I wanted to conduct a test to see how much they really did in high school
Conducted a hypothesis test designed to test how many extracurricular activities students participated in during high school
Study Set-up
Decided that a typical number of extra-curricular activities to participate in during high school is 4
Believed that Notre Dame students typically participated in in a number different than four
So, set up hypothesis test with assumption that the population average was 4 extracurricular activities
Population of Interest:
University of Notre DameUndergraduate Students
Test Design
A commonly held belief is that the average number of clubs, sports, or other school-sponsored extracurricular activities that Notre Dame students participated in during high school is 4
I will test the alternative hypothesis that the number of clubs, sports, or other extracurricular activities that Notre Dame students participated in during high school is not equal to 4
Test Hypotheses
Ho: μ = 4
Ha: μ ≠ 4 μ= Average number of extracurricular
activities participated in during high school
Test at a 95% confidence level
So α = .05
Collecting data
Needed data for test sample
Stood inside front entrance of dining hall during lunch
Randomly administered 50 surveys total Every tenth person
Gave out 25 surveys at each dining hall
Explained any questions respondents may have had
Survey
How many sports, clubs, or school-sponsored extra-curricular activities did you participate in during high school? (Do not double-count activities. For example, if you played football for all four years of high school or were in the same club all four years, it counts as just one activity)
Assumptions of Hypothesis Test
1) The sample is chosen randomly
2) n ≥ 30
Avoiding Bias
Selection Bias Conducted surveys at lunch Conducted surveys at both dining halls
Non-Response Bias Anonymous survey, so no fear of answering All subjects feel comfortable and protected
Measurement Error No biased questions in survey Was there to clear up any questions or confusion
Survey Results- Frequency Distribution
1 2 3 4 5 6 7 8 9 10 110
1
2
3
4
5
6
7
8
9
10
Number of HS Extra-Curricular Activities
Number of Extra-Curricular Activities
Fre
quencey
Sample Data
Sample Mean (X-Bar) = 6.28
Sample Mode= 4, 7 Each occurred nine times
s = 2.3215
n = 50
Test Statistic
Z Distribution
Z = (X-Bar – μo)/( s / √(n))
Z = (6.28 – 4) / (2.3215 / √50)
Observed Z-Value = 6.9447
Decision Rule
We reject the Ho if the observed Z-Value > Z.05/2 = Z.025
Z.025 = 1.96
We reject the Ho if the observed Z-Value > 1.96
Decision
Observed Z-Value = 6.9447 > 1.96
So we reject the Ho
We conclude that the mean number of extracurricular activities that Notre Dame students participated in during high school is not equal to 4
Confidence Interval
95% confidence interval for the true mean number of extracurricular activities
X-bar ± Z.025 ( s / √(n))
6.9447 ± 1.96(2.3215 / √50)
(6.3012, 7.5882)
I am 95% confident that the true mean number of extracurricular activities that Notre Dame students participated in during high school is between 6.3012 and 7.5882 activities