5.14 SAT scores: SAT scores of students at an Ivy League college are distributed with a standard deviation of 250 points. Two statistics students, Raina and Luke, want to estimate the average SAT score of students at this college as part of a class project. They want their margin of error to be no more than 25 points. (a) Raina wants to use a 90% con dence interval. How large a sample should she collect? Raina should sample at least _________ people. (b) Luke wants to use a 99% con dence interval. Without calculating the actual sample size, determine whether his sample should be larger or smaller than Raina's, and explain your reasoning. ( )smaller because higher degrees of confidence require smaller margins of error ( )smaller since Luke has a higher level of confidence in his results than Raina ( )larger higher degrees of confidence require larger margins of error
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
5.14 SAT scores: SAT scores of students at an Ivy League college are distributed with a standard deviation of 250 points. Two statistics students, Raina and Luke, want to estimate the average SAT score of students at this college as part of a class project. They want their margin of error to be no more than 25 points.
(a) Raina wants to use a 90% con dence interval. How large a sample should she collect?
Raina should sample at least _________ people.
(b) Luke wants to use a 99% con dence interval. Without calculating the actual
- ( )smaller because higher degrees of confidence require smaller margins of error
- ( )smaller since Luke has a higher level of confidence in his results than Raina
- ( )larger higher degrees of confidence require larger margins of error
(c) Calculate the minimum required sample size for Luke.
Luke should sample at least ______ people.
The margin of error for a distribution that is assumed to be distributed Normally is given by,
Trending now
This is a popular solution!
Step by step
Solved in 4 steps
