Download Quiz Solutions for MATH 1530 – Chapter 6 - Prof. David W. Carter and more Quizzes Probability and Statistics in PDF only on Docsity!
MATH 1530 – Quiz # 16 (Quizpak 6) Name _____________________________
Ex. 1&2: If women’s heights are normally distributed and a given sample yields
x 63.85 and^
s 2.35 , find a 98% confidence interval for the mean if the following is
true:
1. If n = 19. / 2
z
or^ / 2
t
= ______________
(circle one)
General Formula: _____________________________________________________________
Specific Formula: _____________________________________________________________
Numerical Formula: ___________________________________________________________
Concluding Statement: We are ____________% confident that the true population mean
for women’s heights is between __________________ and _________________ inches.
2. If n = 69. / 2
z
or^ / 2
t
= ______________
(circle one)
General Formula: _____________________________________________________________
Specific Formula: _____________________________________________________________
Numerical Formula: ___________________________________________________________
Concuding Statement: _________________________________________________________
____________________________________________________________________________
MATH 1530 – Quiz # 17 (Quizpak 6) Name _____________________________
- A psychologist has developed a new test of spatial perception, and she wants to estimate the mean
score achieved by male pilots. How many people must she test if she wants the sample mean to be
in error by no more than 2.0 points, with 95% confidence? An earlier study suggests that 21.
General Formula: n = __________________________________________________________
Specific Formula: n = __________________________________________________________
Numerical Formula: n = ________________________________________________________
Concuding Statement: _________________________________________________________
____________________________________________________________________________
- The West America Communications Company is considering a bid to provide long-distance phone
service. You are asked to conduct a poll to estimate the percentage of consumers who are satisfied
with their current long-distance phone service. You want to be 90% confident that your sample is
within 2.5 percentage points of the true population proportion, and a Roper poll suggests that this
percentage should be about 85%. How large must your sample be?
General Formula: n = __________________________________________________________
Specific Formula: n = __________________________________________________________
Numerical Formula: n = ________________________________________________________
Concuding Statement: _________________________________________________________
____________________________________________________________________________
The following notes will be provided for your reference as the last page of Exam 4:
There will be 8 problems on exam 4. One of which is a problem that does not fit a method taught in
Chapter 6. This problem must be identified and N/A should be written on that page. For the other 7
problems, students must be prepared to write the appropriate General Formula , Specific Formula ,
Numerical Value (Do Not Round), and a Concluding Statement (Round values to 4 decimal places).
All work may be done by calculator and can be verified on Statdisk.
- To find a confidence interval for a mean given a large sample (n>30) from any type of distribution,
use 2
z
2 2
x z x z
n n
or if^ ^ is unknown, use:
2 2
s s
x z x z
n n
- To find a confidence interval for a mean given a small sample from a normally distributed
population where ^ is known, use:
2 2
x z x z
n n
- To find a confidence interval for a mean given a small sample from a normally distributed
population where
is unknown, use:
2 2
s s
x t x t
n n
- To find a confidence interval for a mean given a small sample that is NOT from a normally
distributed population, use Nonparametric and Bootstrap methods taught in Chapter 13. For all such
problems we will just write N/A for now.
- To determine the sample size necessary for estimating a mean use:
2
2
z
n
E
- To find a confidence interval for a proportion use:
2 2
pq pq
p z p p z
n n
- To determine the sample size necessary for estimating a proportion where an estimate of
p is given,
use:
2
2
2
z pq^ ˆ ˆ
n
E
- To determine the sample size necessary for estimating a proportion where an estimate of
p is NOT
given, use:
2
2
2
z .5.
n
E
MATH 1530VT1 - Individual Projects - Parts 1-
Experiment: Collect heights in inches from randomly selected adults (18 and
older) from the greater Knoxille, Tennessee area. If you are a male
collect heights from 32 males. If you are a female, collect heights
from 32 females.
Objective Part 1: Determine from your random sample the best point estimate for the
population mean height and the standard deviation in inches.
Results: Print the Descriptive Statistics from Statdisk for your data set and
provide a cover page that explains in a brief paragraph the purpose of
the experiment. In a second paragraph, write your results, namely the
sample mean and the sample standard deviation as your best point
estimates for each respective population parameter. Be sure to
include a title.
Objective Part 2: Determine from your random sample the best interval estimate for
the true population mean height. Create a 95% confidence interval.
Results: Print the Confidence Interval from Statdisk using the mean and
standard deviation from Part 1. Provide the same cover page as used
in Part 1 with a third paragraph that states your confidence interval
in a complete sentence.
Objective Part 3: Conduct a hypothesis test on the mean at the ^ .05^ significance
level.
Males use: 0
H : 69.0 inches
Females use: 0
H : 63.6 inches
Results: Print the Hypothesis Test results from Statdisk using the mean and
standard deviation from Part 1. Provide the same cover page as used
in both part 1 and part 2 with a fourth paragraph that states your
conclusion from the hypothesis test in a complete sentence.
NOTE: You will be graded mostly on the wording used and the accuracy of
your three concluding statements, so be very thorough and use the
appropriate “statistical language”.
DUE DATES are Wed. 7/7 for Part 1, Wed. 7/14 for Part 2, & Sat. July 17 for Part 3.
