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M6D1 - Hypothesis Test Involving the Mean
Generated Jul 17, 2019 by pdugger76

Introduction

The purpose of the survey designed by group two (2) was to examine the habits related to cellular phone video game usage of the average American.  The population that the group members were able to obtain a sample from consisted of family, friends, and co-workers with ages ranging from thirteen (13) to ninety-eight (98).  Collection of survey data was obtained in person and by utilizing social media platforms (i.e., Facebook) – a convenience sample.  All responses were given on a voluntary basis and all respondent’s identifying information was held confidential.  The following questions were included in our survey:

1.Do you play video games on your cell phone? Circle one: yes no

2.What type of game do you usually play? Select one category: 

      Action/Adventure 

      Puzzle

      Role-Playing

      Sports

      Strategy

      Other

      I do not play video games on my phone.

3.How many hours a week do you spend playing video games on your cell phone?

4.What is your age in years?

Explanation of Data Variable for Investigation: Age

The data variable that I am investigating for this week’s activity is ‘Age’.  A prior survey identified the greatest age demographic for video game engagement was the 18-24 category (Morris, 2018).  I will be using my data to examine the claim that individuals who engage in video games on a cellular device have a mean age that is greater than 41.  

The following hypothesis was constructed to compare survey results:

H₀: μ = 41

H₁: μ > 41

Hypothesis Test for Random Sample of n=50

a.Degrees of Freedom, n-1 = 49

b.Value t₀.₀₂ = 2.1098727 (right-tailed test)

c.Results from the hypothesis test: 

<result1>

d.Test statistic, t₀: 0.18424744

e.P-value = 0.4273

f.Sample size = 50
        Sample mean = 41.44
        Sample standard deviation = 16.886367

g.Classical method (conclusion):

Because the test stat, t = 0.184, does not fall in the critical region, 2.110 we fail to reject H₀.

h.P-value method (conclusion):

Using the P-value of 0.4273 and table A-2, a comparison shows that the sample test statistic falls to the left or outside of the critical region.  Result is the same as the conclusion from the classical method test, and we fail to reject the null hypothesis, H₀. 

Hypothesis Test for Complete Data, n= 123

a.Degrees of Freedom, n-1 = 122

b.Value t₀.₀₂ =  2.0759394 (right-tailed test)

c.Results from the hypothesis test:

<result2>

d.Test statistic, t₀: - 0.036138383

e.P-value = 0.5144

f.Sample size = 123
        Sample mean = 40.943089
        Sample standard deviation = 17.465329

g.Classical method (conclusion):

Because the test stat, t = - 0.036, does not fall in the critical region, 2.076 we fail to reject H₀.  The result for the n=123 reached the same conclusion as the n=50 hypothesis test.

The conclusions make sense to me on a basic level; reject hypothesis if the value falls in the critical region and fail to reject if the value does not fall in the critical region.  The hypotheses were constructed to determine if the evidence (μ > 41) was true as the data supported this claim.

References

Morris, C. P. (2018, April 19). The demographics of video gaming. Earnest. Retrieved from https://www.earnest.com/blog/the-demographics-of-video-gaming/

Triola, M. F. (2015). Essentials of statistics (5th ed.). Upper Saddle River, NJ: Pearson.

StatCrunch. (2019). M6D1 – Hypothesis test involving the mean. Retrieved from https://www.statcrunch.com/5.0/viewreport.php?reportid=88441">M6D1 - Hypothesis Test Involving the Mean

Result 1: One sample T hypothesis test   [Info]

One sample T hypothesis test:


μ : Mean of variable
H0 : μ = 41
HA : μ > 41

Hypothesis test results:
VariableSample MeanStd. Err.DFT-StatP-value
Age41.442.3880929490.184247440.4273



Result 2: One sample T hypothesis test for Entire Video Game Data, Age   [Info]

One sample T hypothesis test:


μ : Mean of variable
H0 : μ = 41
HA : μ > 41

Hypothesis test results:
VariableSample MeanStd. Err.DFT-StatP-value
Age40.9430891.5747957122-0.0361383830.5144