Post on 24-Jan-2022
Sample problems:
1. A study was conducted to investigate some effects
of physical training. At 0.05 level of significance, test
the claim that the mean pre-training weight equals
the mean post-training weight. The weights are in
kilograms. What do you conclude about the effect
of training weight?
Pre-training weight :
99 57 62 69 74 77 59 92 70 85
Post-training weight :
94 57 62 69 66 76 58 88 70 84
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2. A dose of the drug Captropil, designed to
lower systolic blood pressure, is administered to
10 randomly selected volunteers, with the
following results. Test the effectiveness of the
drug.
Systolic blood pressure before pill :
120 136 160 98 115 110 180 190 138 128
Systolic blood pressure after pill:
118 122 143 105 98 98 180 175 105 112
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Sample problems:
1. Two methods of teaching statistics are being tried
by a professor. A class of 40 students is taught by
the method A and a class of 36 is taught by
method B. The two classes are given the same final
examination. The mean scores are 78 and 74,
respectively. Using a 0.05 significance level, can we
conclude that the average final examination
scores produced by the two methods are different
if the population standard deviation for each is 5?
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2. In a study of abstract reasoning, a sample
group of male and female students scored
as shown below. Assuming that the
samples are random, would further testing
of similar groups of male and female
students give virtually the same result?
Sex Sample size Mean SD
Male 95 29.21 11.56
Female 83 30.92 7.81
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THE ‘RULE’ OF 2.5
Divide the higher variance by the lower
variance of the two independent
samples.
If the ratio is less than 2.5, use the formula
for equal variance
If the ratio is at least 2.5, use the formula for
unequal variance
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Sample problems:1. The Telektronic Company manufactures car
batteries with two different production methods.
The lives in years of the batteries are found for a
sample of from each group. At 0.05 level of
significance, test the claim that the two
production methods yield batteries with the same
mean.
Methods Sample size Mean St. Dev.
Traditional 29 4.31 0.37
Experimental 27 4.07 0.31
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2. A teacher wishes two methods of teaching
verbs to his Spanish class. He divided the class
randomly into two samples with 14 students
each. Using method 1, the students learn an
average of 43.8 verbs while method 2 yield
an average of 38.6 verbs each with a
standard deviation of 5.2. Theory suggest that
method 1 is superior to method 2. Test the
theory using 0.01 level of significance.
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Sample problems
1. The Gleanson Supermarket’s manager experiments with
two methods of checking out customers. One method
requires that the cashier manually key each price into
their register, and the other method uses a scanner that
automatically registers prices. The time in minutes are
given below for sample of goods checked out. At 0.01
level, test the claim that the two methods have the same
mean.Methods Sample size Mean Variance
Manual 16 157.6 225
Scanning 10 112.4 56
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2. The Wisconsin Bottling Company employs two
shifts of workers to fill bottle with iced tea. Test
the claim that there is no significant difference
between the mean fill amount for the day shift
and the night shift at 5% level of significance.
Shift Sample size Mean St. Dev.
Day 25 12.02oz. 0.14oz.
Night 28 11.85oz. 1.22oz.
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Problem 1:
At the beginning of the school year, the mean
score of the group of 24 students in an
educational achievement test in reading was
45 with standard deviation of 6. At the end of
the school year, the mean score on an
equivalent for of test was 50 with standard
deviation of 5. Did the class make a significant
progress in reading during this year? Use alpha
0.05.
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Problem 2: cars radial tires belted tires1 4.2 4.12 4.7 4.93 6.6 6.24 7 6.95 6.7 6.86 4.5 4.47 5.7 5.78 6 5.89 7.4 6.9
10 4.9 4.711 6.1 612 5.2 4.9
A taxi company is trying to
decide whether the use of
radial tires instead of regular
belted tires improves fuel
economy. Twelve cars were
driven twice over a
prescribed test course, each
time using a different type of
tires (radial and belted) in
random order. The mileage, in
kilometers per liter were
recorded.
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Problem 3:
subject Before After
A 6.6 6.8
B 6.5 2.4
C 9 7.4
D 10.3 8.5
E 11.3 8.1
F 8.1 6.1
G 6.3 3.4
H 11.6 2
Based on “An Analysis of Factors That
Contribute to the Efficacy of Hypnotic
Analgesia”, by Price and Barber,
Journal of Abnormal Psychology, Vol.
96, No. 1. A study was conducted to
investigate the effectiveness of
hypnotism in reducing pain. Results for
randomly selected subjects are given
below. At 0.01 level of significance, test
the claim that the sensory
measurements are lower after
hypnotism. Does hypnotism appear
effective in reducing pain?
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