try For one part of the study n 114 male athletes from eigh

For one part of the study, n = 114 male athletes from eight Canadian sports centers were surveyed. Their average caloric intake was 3077.0 kilocalories per day (kca/ with a standard deviation of 987.0. The recommended amount is 3421.7. Is there evidence that Canadian high-performance male athletes are deficient in their caloric intake? State the appropriate H0 and Ha to test this. Carry out the test, give the P-value, and state your conclusion. Construct a 95% confidence interval for eficiency in caloric intake.

Solution

a)

Formulating the null and alternative hypotheses,              
              
Ho:   u   >=   3421.7  
Ha:    u   <   3421.7   [ANSWER]

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B)

              
As we can see, this is a    left   tailed test.      
              
Thus, getting the critical z, as alpha =    0.1   ,      
alpha =    0.1          
zcrit =    -   1.281551566      
              
Getting the test statistic, as              
              
X = sample mean =    3077          
uo = hypothesized mean =    3421.7          
n = sample size =    114          
s = standard deviation =    987          
              
Thus, z = (X - uo) * sqrt(n) / s =    -3.728864107          
              
Also, the p value is              
              
p =    0.0000961724   [ANSWER, P VALUE]      
              
Comparing z and zcrit (or, p < 0.05), we   REJECT THE NULL HYPOTHESIS.          

Thus, there is significant evidence that Canadian high-performance male athletes are deficient in their caloric intake.

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C)

Note that              
              
Lower Bound = X - z(alpha/2) * s / sqrt(n)              
Upper Bound = X + z(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.025          
X = sample mean =    3077          
z(alpha/2) = critical z for the confidence interval =    1.959963985          
s = sample standard deviation =    987          
n = sample size =    114          
              
Thus,              
              
Lower bound =    2895.818931          
Upper bound =    3258.181069          
              
Thus, the confidence interval is              
              
(   2895.818931   ,   3258.181069   ) [ANSWER]