try For one part of the study, n = 114 male athletes from eight Canadian sports
ID: 3442820 • Letter: T
Question
try 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.Explanation / Answer
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]
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