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.
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