For your study on food consumption habits of teenage males y

For your study on food consumption habits of teenage males, you randomly select 10 teenage male and ask them how many 12 ounce servings of soda he drinks each day. The results are listed below. At a=0.10, is there enough evidence to support the claim that the teenage male drinks fewer than three 12 ounce servings per day? Assume the population is normally distrubuted. 3.9, 2.7, 2.6, 2.2, 1.5, 3.4, 2.5, 3.1, 3.1, 1.3 (a) Write the claim mathematically and identify Ho and Ha. (b) Use technology to find P. (c) Decide whether to reject or fail to reject the null hypothesis. (d) Intrepret the decision in the contex of the original claim.

Solution

a)

Claim: u < 3

Formulating the null and alternative hypotheses,              
              
Ho:   u   >=   3  
Ha:    u   <   3   [ANSWER]

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b)
              
As we can see, this is a    left   tailed test.      
              
df = n - 1 =    9          
              
Getting the test statistic, as              
              
X = sample mean =    2.63          
uo = hypothesized mean =    3          
n = sample size =    10          
s = standard deviation =    0.809732466          
              
Thus, t = (X - uo) * sqrt(n) / s =    -1.444974462          
              
Also, the p value is, as this is left tailed,              
              
p =    0.091182933   [ANSWER]

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c)

As P < 0.1, we   REJECT THE NULL HYPOTHESIS.      

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d)

Hence, there is significant evidence to support that claim hat the teenage male drinks fewer than three 12 ounce servings per day. [CONCLUSION]