The ability to read rapidly and simultaneously maintain a high level of comprehe

Question

The ability to read rapidly and simultaneously maintain a high level of comprehension is often a determining factor in the academic success of many high school students. A school district is considering a supplemental reading program for incoming freshmen. Prior to implementing the program, the school runs a pilot program on a random sample of n = 20 students. The students were thoroughly tested to determine reading speed and reading comprehension. Based on a fixed-length standardized test reading passage, the following reading times (in minutes) and increases in comprehension scores (based on a 100-point scale) were recorded. a. Place a 95% confidence interval on the mean reading time for all incoming freshmen in the district.

Explanation / Answer

a)

Note that              
Margin of Error E = t(alpha/2) * s / sqrt(n)              
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 =    0.025          
X = sample mean =    9.1          
t(alpha/2) = critical t for the confidence interval =    2.093024054          
s = sample standard deviation =    2.573          
n = sample size =    20          
df = n - 1 =    19          
Thus,              
Margin of Error E =    1.204201068          
Lower bound =    7.895798932          
Upper bound =    10.30420107          
              
Thus, the confidence interval is              
              
(   7.895798932   ,   10.30420107   ) [ANSWER]

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