Psychology 290
Research Methods & Statistics
Lab 11
z-tests and t-tests
March 5 – 7, 2007
1.
The national average (μ) on the Verbal subtest of the Scholastic Aptitude Test (SAT-V) is
500 with a standard deviation (σ) of 100. If a sample of 36 students who were homeschooled had an average SAT-V score of 540, should we conclude that home-schooled
students have significantly higher verbal skills? Use α=.05 and conduct the appropriate twotailed test.
z = (X – )  540 – 500  40 = 2.40
(/ √n)
(100/√36)
16.67
zcrit (α=.05, two tail) = 1.96
zobt > zcrit therefore, we can reject the null.
(2.4 > 1.96)
The students who were home-schooled performed significantly better (i.e. had higher verbal
skills) than those who were not home-schooled.
2.
We randomly select a group of 9 subjects from a population with a mean () IQ of 100 and
standard deviation () of 15. We give the subjects intensive "Get Smart" training and then
administer an IQ test. If the sample’s mean IQ was 121, can you conclude that the training
resulted in a significant increase in IQ score? Use α=.05 and conduct the appropriate test.
z = (X – )  (121 – 100)  21 = 4.20
(/ √n)
(15/√9)
5
zcrit (α=.05, one tail) = 1.64
zobt > zcrit therefore, we can reject the null.
(4.2 > 1.64)
Those who underwent training acquired significantly higher IQ scores compared to those
who did not receive the special training.
3.
At 36 months of age, the average child can put 3.6 words together in a sentence (this is
known as mean length of utterance, or MLU). If the average MLU for a sample of 12 abused
children was found to be 2.9 and a standard deviation of 0.76, would we conclude that abused
children’s language development is significantly delayed? Use α =.05 and conduct the
appropriate two-tailed test.
t = (X – )  2.9 – 3.6  -0.7 = -3.18
(s/ √n)
(0.76/√12) 0.22
tcrit (α =.05, two-tailed, df=11) = 2.201
| tobt | > tcrit, therefore we can reject the null
df = n – 1 = 12 – 1 = 11
Abused children’s language development is significantly delayed compared to non-abused
children.
4.
The average weight of a sheep brain is 140 grams. In a biopsychology lab that uses sheep
brains for dissecting and demonstration purposes, a new shipment of 25 brains arrived that
seemed oddly oversized. The sample of brains had a mean size of 200 grams with a standard
deviation of 20. Determine whether these brains came from the standard population of sheep
or are perhaps from some population of super-intelligent sheep. Use α =.05 and conduct the
appropriate test.
t = (X – )  200 – 140  60 = 15.0
(s/ √n)
(20/√25)
4
df = n – 1 = 25 – 1 = 24
tcrit (α =.05, one-tailed, df=11) = 1.711
| tobt | > tcrit, therefore we can reject the null
The new shipment of brains did come from a significantly different population of sheep.
These brains were significantly larger than the standard sheep brains. Relevant
5.
Four small classes of Psych 100 just completed their first term of course work. At the end of
the winter term, the Nation-wide mean for Psych 100 classes is 72.4. The professor from each
section wanted to see if their classes were different than the Nation wide norm. Below are the
grades for all the students in each of the four classes. Use SPSS to conduct a one sample t-test
on each class to determine whether the following samples come from the normal population
or not.
Psych 100:11
54
85
80
71
69
72
43
59
75
70
60
Psych 100:12
51
56
65
79
42
59
64
70
55
Psych 100:13
83
84
69
73
65
59
89
81
91
78
80
Psych 100:14
95
40
45
85
70
55
50
92
84
68
One-Sample Statistics
N
Std. Deviation
12.11986
Std. Error
Mean
3.65427
11
Mean
67.0909
Psych10012
9
60.1111
10.89087
3.63029
Psych10013
11
77.4545
9.98362
3.01018
Psych10014
10
68.4000
20.16157
6.37565
Psych10011
One-Sample Test
Test Value = 72.4
95% Confidence Interval
of the Difference
df
Mean
Difference
-5.30909
Lower
-13.4513
Psych10011
t
-1.453
10
Sig. (2-tailed)
.177
Upper
2.8331
Psych10012
-3.385
8
.010
-12.28889
-20.6604
-3.9174
Psych10013
1.679
10
.124
5.05455
-1.6525
11.7616
Psych10014
-.627
9
.546
-4.00000
-18.4227
10.4227
Classes 11, 13, and 14 are not significantly different than the Nation-wide norm. None of the
significant values for those three samples (0.177, 0.124, and 0.546, respectively) are less than the
pre-set alpha level of 0.05. On the other hand, the Psych 100:12 does seem to be significantly
different than the normal population (0.01 is less than 0.05). Also, looking at the sample means,
you can infer that the Psych 100:12 class had a significantly lower average grade than the norm
(average of 60.1 was significantly lower than the population mean of 72.4).