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(20.60 S-AQ) To study the metabolism of insects, researchers fed cockroaches mea

ID: 3157253 • Letter: #

Question

(20.60 S-AQ) To study the metabolism of insects, researchers fed cockroaches measured amounts of a sugar solution. After 2, 5, and 10 hours, they dissected some of the cockroaches and measured the amount of sugar in various tissues. Five roaches fed the sugar D-glucose and dissected after 10 hours had the following amounts (in micrograms) of D-glucose in their hindguts:

The researchers gave a 98% confidence interval for the mean amount of D-glucose in cockroach hindguts under these conditions. The insects are a random sample from a uniform population grown in the laboratory. We therefore expect responses to be Normal.

The mean (±0.01) and the standard deviation (±0.0001) of the SRS are:   
x¯ =      s = .


The critical value (±0.001) from the distribution for 98% confidence interval is:   
t* = .


What confidence interval (±0.01) did the researchers give?    to    .

(20.60 S-AQ) To study the metabolism of insects, researchers fed cockroaches measured amounts of a sugar solution. After 2, 5, and 10 hours, they dissected some of the cockroaches and measured the amount of sugar in various tissues. Five roaches fed the sugar D-glucose and dissected after 10 hours had the following amounts (in micrograms) of D-glucose in their hindguts:

Amounts of D-glucose   55.95 68.24 52.73 21.5 23.78

The researchers gave a 98% confidence interval for the mean amount of D-glucose in cockroach hindguts under these conditions. The insects are a random sample from a uniform population grown in the laboratory. We therefore expect responses to be Normal.

The mean (±0.01) and the standard deviation (±0.0001) of the SRS are:   
x¯ =      s = .


The critical value (±0.001) from the distribution for 98% confidence interval is:   
t* = .


What confidence interval (±0.01) did the researchers give?    to    .

Explanation / Answer

By technology,

X = sample mean =    44.44   [ANSWER]      

s = sample standard deviation =    20.74080158   [ANSWER]

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As

alpha/2 = (1 - confidence level)/2 =    0.01      

df = n - 1 = 4, by table/technology for alpha/2 = 0.01,

t(alpha/2) = critical t for the confidence interval =    3.747   [ANSWER]

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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 =    44.44          
t(alpha/2) = critical t for the confidence interval =    3.746947388          
s = sample standard deviation =    20.74080158          
n = sample size =    5          
df = n - 1 =    4          
Thus,              
              
Lower bound =    9.684933039          
Upper bound =    79.19506696          
              
Thus, the confidence interval is              
              
(   9.684933039   ,   79.19506696   )

or

(   9.68   ,   79.20   ) [ANSWER]