1. The following sample is a sample of blood glucose levels taken from 10 childr

Question

1. The following sample is a sample of blood glucose levels taken from 10 children aged 14 – 16 who report that they routinely eat fast food three or more times a week.

100 99 97 104 124 120 89 122 118 101

a)Because of the small sample size, what assumption must be true before a confidence interval can be constructed for the population average?

Write a complete sentence.

b)Assuming what you wrote in part (a) is true and that the population standard deviation is known to be 5, construct and interpret a 98% confidence interval for the average blood glucose levels for children aged 14-16 who report that they routinely eat fast food.

c) Assuming what you wrote in part (a) is true and that the population standard deviation is unknown, construct and interpret a 98% confidence interval for the average blood glucose levels for children aged 14-16 who report that they routinely eat fast food.

Explanation / Answer

1.

a) The population from which this data came from must be approximately normally distributed.

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b)

Note that              
              
Lower Bound = X - t(alpha/2) * s / sqrt(n)              
Upper Bound = X + t(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.01          
X = sample mean =    107.4          
t(alpha/2) = critical t for the confidence interval =    2.821437925          
s = sample standard deviation =    5          
n = sample size =    10          
df = n - 1 =    9          
Thus,              
              
Lower bound =    102.9389149          
Upper bound =    111.8610851          
              
Thus, the confidence interval is              
              
(   102.9389149   ,   111.8610851   ) [ANSWER]

***************

c)

Note that              
              
Lower Bound = X - t(alpha/2) * s / sqrt(n)              
Upper Bound = X + t(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.01          
X = sample mean =    107.4          
t(alpha/2) = critical t for the confidence interval =    2.821437925          
s = sample standard deviation =    12.40250871          
n = sample size =    10          
df = n - 1 =    9          
Thus,              
              
Lower bound =    96.33427074          
Upper bound =    118.4657293          
              
Thus, the confidence interval is              
              
(   96.33427074   ,   118.4657293   ) [ANSWER]

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