A nutrition expert claims that the average American is overweight. To test his c

Question

A nutrition expert claims that the average American is overweight. To test his claim, a random sample of 25 Americans was selected, and the difference between each person's actual weight and ideal weight was calculated. For this data, we have x=15.5 and s=29. Is there sufficient evidence to conclude that the expert's claim is true? Carry out a hypothesis test at a 8% significance level. (You may assume a normally distributed population.)

A. The value of the standardized test statistic:

B. The p-value is

Explanation / Answer

a)

Formulating the null and alternative hypotheses,              
              
Ho:   u   <=   0  
Ha:    u   >   0  
              
As we can see, this is a    right   tailed test.      
              
              
Getting the test statistic, as              
              
X = sample mean =    15.5          
uo = hypothesized mean =    0          
n = sample size =    25          
s = standard deviation =    29          
              
Thus, z = (X - uo) * sqrt(n) / s =    2.672413793 [ANSWER]

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B)          
              
Also, the p value is, as this is right tailed,              
              
p =    0.003765386   [ANSWER]      
      
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As P < 0.08, we   REJECT THE NULL HYPOTHESIS.          

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