Chapter 11 Practice Test Free responses:
Nitrites are often added to meat products as preservatives. In a study of the effect of these
chemicals on bacteria, the rate of uptake of a radio-labeled amino acid was measured for a
number of cultures of bacteria, some growing in a medium to which nitrites had been added.
Here are the summary statistics from this study.
x
Group
n
s
Nitrite
Control
30
30
7880
8112
1115
1250
7. Carry out a test of the research hypothesis that nitrites decrease amino acid uptake and
report your results.
Step 1: Let the population 1 be all cultures of bacteria which might be
treated with nitrite and let population 2 be all cultures of bacteria which
go untreated. We want to test a claim about the mean amino acid uptakes
in these two populations.
H 0 : µ1 = µ2
or
H 0 : µ1 − µ2 = 0
H a : µ1 > µ2
or
H a : µ1 − µ2 > 0
Step 2: The cultures were randomly allocated to the two treatment
groups. The large sample sizes should assure the approximate normality
of the sampling distribution of x1 - x 2
Step 3:
t =
t =
( x1 − x2 ) − ( µ1 − µ 2 )
2
2
s1
s
+ 2
n1 n2
( 7880−8112 )−(0 )
11152 1250 2
+
30
30
t = -.7586
.683 < .7586 < .854
.20 <
P-value( t(29) > .7586 ) < .25
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Using the calculator:
Stat/Tests/2-SampleTTest
Step 4: There is insufficient evidence to reject H0 . We can’t conclude
that nitrites decrease amino acid uptake.
8 Do various occupational groups differ in their diets? A British study of this question
compared 98 drivers and 83 conductors of London double-decker buses. The
conductors’ jobs require more physical activity. The article reporting the study gives
the data as “Mean daily consumption ( ± se).” Some of the study results appear
below.
(a) Give x and s for each of the alcohol measurements.
Alcohol: 0.06 = s / sqrt(98)
s = 0.59
Drivers
Calories
Alcohol
x
2821
0.24
Conductors
s
534.6
0.59
x
2844
0.39
s
437.3
1.00
2
(b) Construct a 95% confidence interval for the mean daily alcohol consumption of
London double-decker bus conductors. Follow the Inference Toolbox.
The 95% confidence interval for the mean daily alcohol consumption of
double-decker conductors is (0.28,0.50). Assumption: SRS. However, the
sample was large enough to make use of the CLT to assume normality.
(c) Construct a 99% confidence interval for the difference in mean daily alcohol consumption
between drivers and conductors.
The 99% confidence interval for µ C - µ D is (0.39 – 0.24) ± 2.637 0.06 2 + 0.112 =
( -0.18,0.48)
9. The National Endowment for the Humanities sponsors summer institutes to improve the
skills of high school teachers of foreign languages. One such institute hosted 20 French
teachers for four weeks. At the beginning of the period, the teachers were given the Modern
Language Association’s listening test of understanding of spoken French. After four weeks of
immersion in French in and out of class, the listening test was given again. (The actual French
spoken in the two tests was different, so that simply taking the first test should not improve the
score on the second test.) Table 7.1 gives the pretest and posttest scores. The maximum
possible score on the test is 36.
We hope to show that attending the institute improves listening skills. Carry out an
appropriate test of this claim at the α = 0.05 level.
Step 1: Let X = post-test score – pre-test score.
This is a matched paired design.
We want to test H0 : µ = 0 the mean score of all French teachers who would
enroll in this summer course.
Ha : µ > 0
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Step 2: Conditions
1. SRS - assumption
2. Normality?
There is a slight left skew and no outliers. We are not greatly concerned
about a small amount of skewness with a sample size of 20.
Step 3:
Using the calculator: put the values of X into list1/L1 on the TI-83/89, we
get t = 6.307, and P-value = 0.000.
We can reject H0 at the 5% level of significance, and at the 1% level.
Note that n = 20, x = 3.1, s = 2.198 and df = 19
Step 4: Since we reject the H0 at the 1% level of significance, it is
obvious that attending the institute improves listening skills
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