18 18 18 19 19 19 19 19 19 19 19 19 19 20 20 20 20 21 21 21 22 22 22 23 24 26 28 31 32 36 41 44 1) Find a 98% confidence interval for the mean age of PSU Stat 243 students (and record the bounds to 2 decimal places). Do the median and mode fall into this range? If we want the margin of error to be less than 1 year, how many total students should we sample? 2) Someone once told me that the average age of PSU students is 27. Does this value fall within the confidence interval? Assuming that this is the true mean age with a standard deviation of σ=6, what is the probability of seeing a mean age (of a sample of n=32) less than 24? Does this provide evidence that the true mean of PSU stat 243 students is less than 27? Can we generalize this result to all PSU students? (Hint: consider your answer to problem 9 on homework #2.) 3) Find a 90% confidence interval for the proportion of stat 243 students who can legally purchase recreational drugs in the State of Oregon (students who are 21 or over). If we want the margin of error to be within 3 percentage points, how many total students must we sample? 4) If we assume that the data is normal and treat the mean and standard deviation of the sample as if they were the population values, find the probability that a random stat 243 student can purchase recreational drugs, or rather, calculate P(age>20.5). Does this value fall in the confidence interval from problem 3? 5) Based on your answers from problem 1 (regarding the median and mode) and problem 4, along what you observed in homework #2, do we have evidence that the original data is not normal? Considering the CLT and its requirements, does this mean that we are not justified in using the normal distribution for our confidence intervals? Be sure to keep 4 significant digits for all probabilities and proportions.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.3: Measures Of Spread

Problem 1GP

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Stat 243 Fall 2022
Homework #7

18 18 18 19 19 19 19 19 19 19 19 19 19 20 20 20
20 21 21 21 22 22 22 23 24 26 28 31 32 36 41 44
1) Find a 98% confidence interval for the mean age of PSU Stat 243
students (and record the bounds to 2 decimal places). Do the
median and mode fall into this range? If we want the margin of
error to be less than 1 year, how many total students should we
sample?

2) Someone once told me that the average age of PSU students is 27.
Does this value fall within the confidence interval? Assuming
that this is the true mean age with a standard deviation of σ=6,
what is the probability of seeing a mean age (of a sample of
n=32) less than 24? Does this provide evidence that the true
mean of PSU stat 243 students is less than 27? Can we generalize
this result to all PSU students? (Hint: consider your answer to
problem 9 on homework #2.)

3) Find a 90% confidence interval for the proportion of stat 243
students who can legally purchase recreational drugs in the State
of Oregon (students who are 21 or over). If we want the margin
of error to be within 3 percentage points, how many total
students must we sample?

4) If we assume that the data is normal and treat the mean and
standard deviation of the sample as if they were the population
values, find the probability that a random stat 243 student can
purchase recreational drugs, or rather, calculate P(age>20.5).
Does this value fall in the confidence interval from problem 3?

5) Based on your answers from problem 1 (regarding the median and
mode) and problem 4, along what you observed in homework #2, do
we have evidence that the original data is not normal?
Considering the CLT and its requirements, does this mean that we
are not justified in using the normal distribution for our
confidence intervals?
Be sure to keep 4 significant digits for all probabilities and
proportions.

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