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Hypothesis Testing: High School

Extracurricular Activities

ByCasey McCurdy

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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