Statistics for the Behavioral Sciences by Frederick J. Gravetter, Larry B. Wallnau ISBN 10: 1305504917 ISBN 13: 9781305504912

DEMONSTRATION 9.1 293
One-Sample Statistics
N
Mean
Std. Deviation
Std. Error
Mean
VAR00001 9 13.0000
3.00000
1.00000
One-Sample Test
Test Value = 10
95% Confidence Interval of the
Difference
t df Sig. (2-tailed)
Mean
Difference Lower Upper
VAR00001
3.000 8 .017 3.00000 .6940 5.3060
FIGURE 9.9
The SPSS output for the hypothesis test in Example 9.2.
FOCUS ON PROBLEM SOLVING
1. The first problem we confront in analyzing data is determining the appropriate statistical
test. Remember that you can use a z-score for the test statistic only when the value for σ is
known. If the value for σ is not provided, then you must use the t statistic.
2. For the t test, the sample variance is used to find the value for estimated standard error.
Remember that when computing the sample variance, use n – 1 in the denominator (see
Chapter 4). When computing estimated standard error, use n in the denominator.
DEMONSTRATION 9.1
A HYPOTHESIS TEST WITH THE t STATISTIC
A psychologist has prepared an “Optimism Test” that is administered yearly to graduating
college seniors. The test measures how each graduating class feels about its future—the higher
the score, the more optimistic the class. Last year’s class had a mean score of μ = 15. A sample
of n = 9 seniors from this year’s class was selected and tested. The scores for these seniors
are 7, 12, 11, 15, 7, 8, 15, 9, and 6, which produce a sample mean of M = 10 with SS = 94.
On the basis of this sample, can the psychologist conclude that this year’s class has a different
level of optimism than last year’s class?
Note that this hypothesis test will use a t statistic because the population variance (σ 2 ) is
not known.
STEP 1
State the hypotheses, and select an alpha level The statements for the null hypothesis and
the alternative hypothesis follow the same form for the t statistic and the z-score test.
H 0
: μ = 15
H 1
: μ ≠ 15
(There is no change.)
(This year’s mean is different.)
For this demonstration, we will use α = .05, two tails.