You are interested in the amount of time teenagers spend wee

You are interested in the amount of time teenagers spend weekly working at jobs. A random sample of 15 teenagers was drawn and each reported the amount of time spent at pan jobs (in minutes), with the following results: sample mean is 147.3 and sample standard deviation is so. Assume that the population is normally distributed. Is there evidence that the mean amount of time teenagers spend weekly working at part-time jobs is more t an 120 minutes? Use a = 0.05 and the critical value approach to hypothesis testing. State your hypotheses. Which hypothesis test should you use? State your rejection rule and the critical value(s) Calculate the test statistic. State your conclusion.

Solution

I.

Formulating the null and alternative hypotheses,              
              
Ho:   u   <=   120  
Ha:    u   >   120   [ANSWER]

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ii.

A z test, as we assume the population is normally distributed.

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iii.
              
As we can see, this is a    right   tailed test.      
              
Thus, getting the critical z, as alpha =    0.05   ,      
alpha =    0.05          
zcrit =    +   1.644853627      

Hence, reject Ho at z > 1.644853627. [ANSWER]

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iv.      
              
Getting the test statistic, as              
              
X = sample mean =    147.3          
uo = hypothesized mean =    120          
n = sample size =    15          
s = standard deviation =    50          
              
Thus, z = (X - uo) * sqrt(n) / s =    2.114648907 [ANSWER]

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v.          
As z > 1.6449, we   REJECT THE NULL HYPOTHESIS.  

Hence, there is significant evidence at 0.05 level that the mean amount of time teenagers spend weekly working at part-time jobs is more than 120 minutes. [CONCLUSION]