According to a 2013 study done by the Curious Research Group, the mean time stud

Question

According to a 2013 study done by the Curious Research Group, the mean time students under the age of 18 spend on video games per day is 150 minutes with a standard deviation of 26 minutes. A group of concerned parents believe that the actual amount of time spent on video games is much more. A random sample of 100 students under the age of 18 was taken and had a mean time of 172 minutes spent on video games per day. By answering the following questions, you’ll conduct a hypothesis test at the 0.05 significance level to test the parents’ claim that the mean time spent on video games by students is greater than 150 minutes. Use correct symbols in your answers.

a) What is the population mean? ___________ = ___________

b) What is the sample mean? ___________ = ____________

c) What are the null and alternate hypotheses? H0 : ________________________ H1 : _____________________________________

d) Find the test statistic and the critical value. (Calculator is OK, but show your command.) _______________________________________________________________

e) Find the P-value. (Calculator is OK, but show your command.) ________________________________________________________________

f) Based on your answer in part d or e, make a decision about this hypothesis test. Justify your decision. _________________________________________________________________________________________

g) Interpret your decision. Do you think there is enough evidence to support parents’ claim? Use full sentences.

Explanation / Answer

a)

u = 150

b)

X = 172

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c)

Ho: u <= 150
Ha: u > 150 [ANSWER]

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d)

Formulating the null and alternative hypotheses,              
              
Ho:   u   <=   150  
Ha:    u   >   150  
              
As we can see, this is a    right   tailed test.      
Getting the test statistic, as              
              
X = sample mean =    172          
uo = hypothesized mean =    150          
n = sample size =    100          
s = standard deviation =    26          
              
Thus, z = (X - uo) * sqrt(n) / s =    8.461538462 [ANSWER, TEST STATISTIC]

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Thus, getting the critical z, as alpha =    0.05   ,      
alpha =    0.05          

zcrit =    +   1.644853627   [ANSWER, CRTIICAL VALUE]

[You can do invnorm(0.95, 0, 1) on a ti84 here.]

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e)      
              
Also, the p value is              
              
p =    1.31937*10^-17   [ANSWER]

[You can do normcdf(8.46153, 99999999, 0, 1) here.]

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f)

As P < 0.05, we REJECT HO.

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g)      
              
There is significant evidence at 0.05 level that the true mean amount of time spent on video games is more than 150 minutes per day. [ANSWER]

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