STAT 3090
L
AB
S
ECTION
9
P
ART
3
F
ALL
2023
H
YPOTHESIS
T
EST
V
ARIANCE
AND
E
RRORS
N
AME
:
O
BJECTIVES
:
Upon completion of this lab, you should be able to:
State and verify the conditions necessary for a hypothesis test for variance/standard
deviation
Locate the Rejection Region for a hypothesis test for variance/standard deviation using
the chi squared distribution
Perform a Hypothesis Test for a variance/standard deviation
Calculate a P-value for a hypothesis test for a variance/standard deviation
Draw conclusions about the population based on the results of a sample
Describe a Type I and II error in context
1.
N
OODLE
L
ENGTHS
M
ACHINE
#13 (45 pts)
D
IRECTIONS
:
For the following
hypothesis test for variance
, you should define your parameter
of interest and follow the HATS steps to complete the hypothesis test. Address each step in your
answer.
Previously in STAT 3090 …
As you may recall from Labs 8 and 9 (Proportions and Means) and JMP Test 2, one of the
machines that makes the spaghetti noodles for Delectable Delights, machine #13, has been
malfunctioning. The noodles have not been a consistent length.
First the noodles were too long,
and now they are too short.
By this time the employees at Delectable Delights are, well, for lack
of a better term, freaked out.
(They have no idea that the Weasley boys have been using the
machine to test their Too Long Spell and their Too Short Spell.)
A repair service was called and machine #13 was recalibrated to produce noodles with lengths
that are normally distributed and on average 252.5 mm long.
In the JMP Quiz 2, you used a
sample of noodles from Machine #13 to check whether the mean length is within spec. But the
other requirement for noodle manufacture is that the lengths of the noodles should not vary too
much—in particular, the standard deviation of noodle lengths should not exceed
2.3mm.
In a
sample of 65 randomly selected noodles, the standard deviation of noodle lengths was
2.55mm.
Complete a hypothesis test to determine if there is evidence at the 0.05 level that machine #13’s
output is too variable. Write up your result using the HATS procedure (address each of the steps
in your answer). Use P-value approach or the rejection region approach with the appropriate
table from your course notes.
You may assume that the population of noodle lengths is
approximately normally distributed.
Let
σ
2
= the population variance of the length of spaghetti noodles from machine #13
1
