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Randomly selected students participated in an experiment to test their ability t

ID: 3437712 • Letter: R

Question

Randomly selected students participated in an experiment to test their ability to determine when one minute (or sixty seconds) has passed. Forty students yielded a sample mean of 60.4 seconds. Assuming that 10.3 seconds, construct and interpret a 99% confidence interval estimate of the population mean of all students Click here to view a t distribution table Click here to view of the standard norma distribution table age Click here to view page 2 of the standard norma distribution table What is the 99% confidence interval for the population mean H? Type integers or decimals rounded to one decimal place as needed.) Based on the result, is it likely that the students' estimates have a mean that is reasonably close to sixty seconds? O A. No, because the confidence interval includes sixty seconds O B. Yes, because the confidence interval does not include sixty seconds. O C. No, because the confidence interval does not include sixty seconds. O D. Yes, because the confidence interval includes sixty seconds.

Explanation / Answer

Note that              
              
Lower Bound = X - z(alpha/2) * s / sqrt(n)              
Upper Bound = X + z(alpha/2) * s / sqrt(n)              
              
where              
              
X = sample mean =    60.4          
z(alpha/2) = critical z for the confidence interval =    2.575829304          
s = sample standard deviation =    10.3          
n = sample size =    40          
              
Thus,              
              
Lower bound =    56.20507396          
Upper bound =    64.59492604          
              
Thus, the confidence interval is              
              
(   56.20507396   ,   64.59492604   ) [ANSWER]

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OPTION D: Yes, because the confidence interval includes 60 seconds. 60 is between those two numbers.