1 According to a 2013 study done by the Curious Research Gro

1. 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. _________________________________________________________________________________________ __________________________________________________________________________________________

Solution

Set Up Hypothesis
Null, H0: U=150
Alternate, time spent on video games by students is greater than 150 minutes H1: U>150
Test Statistic
Population Mean(U)=150
Given That X(Mean)=172
Standard Deviation(S.D)=26
Number (n)=100
we use Test Statistic (Z) = x-U/(s.d/Sqrt(n))
Zo=172-150/(26/Sqrt(100)
Zo =8.4615
| Zo | =8.4615
Critical Value
The Value of |Z | at LOS 0.05% is 1.64
We got |Zo| =8.4615 & | Z | =1.64
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value : Right Tail - Ha : ( P > 8.4615 ) = 0
Hence Value of P0.05 > 0, Here we Reject Ho
We have evidence to indicate that time spent on video games by students is greater than 150 minutes