Randomly selected students participated in an experiment to

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.

Solution

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.