THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION

question 38

Essay

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
The number of hours spent studying by students on Michigan State campus in the week before final exams follows a normal distribution with standard deviation 9.5 hours.A random sample of these students is taken to estimate the population mean number of hours studying.
-Without doing the calculations,state whether a larger or smaller sample would be required to guarantee that the probability that the sample mean differs from the population mean by more than 1.8 hours is less than 0.05,when compared to the sample needed to ensure that the probability that the sample mean differs from the population mean by more than 2.1 hours is less than 0.05.

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Definitions:

Freshmen

First-year students in a high school, college, or university.

Probability

A quantification of the probability of an event happening, indicated by a value ranging from 0 to 1, with 0 meaning the event cannot happen and 1 meaning the event is certain to happen.

Standard Deviation

A statistic that measures the dispersion or variability of a dataset relative to its mean, indicating how spread out the values are.

Simple Random Sample

An evenly selected portion of a wider population, with each participant having an equal opportunity to be chosen.