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

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 61.8 seconds. Assuming that =10.3 seconds, construct and interpret a 90% confidence interval estimate of the population mean of all students.

What is the 90% confidence interval for the population mean ?

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Based on the result, is it likely that the students' estimates have a mean that is reasonably close to sixty seconds?

A.Yes,because the confidence interval includes sixty seconds.

B.No, because the confidence interval does not include sixty seconds.

C. No, because the confidence interval includes sixty seconds.

D. Yes, because the confidence interval does not include sixty seconds.

Explanation / Answer

Here sample mean x = 61.8 seconds

Population standrd deviation =10.3 seconds

standard error of sample mean =10.3/ n = 10.3/ 40 = 1.6286 secs

Here 90% confidence interval = x +- Z 90% se0 = 61.8 +- 1.645 * 1.6286

= (59.12 sec, 64.48 sec)

so here he confidence interval consisits the value of time = 60 secs so

OPtion A is correct that the mean is resonalby close to sexty seconds, the confidence interval includes sixty seconds.

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