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HOMEWORK - One Sample t-tests on SPSS
I. A principal wonders if her 5th graders score differently on a math test than 5th graders
in the U.S. at large. She gets a random sample of 20 5th graders from her school. She
knows that 5th graders in the U.S. at large have a mean of 88 on the test.
Here are the scores of her sample of 20 5th graders: 75, 92, 85, 66, 93, 88, 75, 90, 90, 92,
84, 88, 67, 98, 99, 100, 79, 95, 88, 89
(mathtest.sav)
HA: μ ≠ 88
H0: μ = 88
Move "mathtest" into Test Variable(s) field - press OK
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SEM = SD/ root of N
= 9.77/ root of 20
= 9.77/4.47
= 2.19 (Same as above under Std. Error Mean
t = (mean of sample - mean of population)/SEM
= (86.65 - 88)/2.19
= -1.35/2.19
= -.62 (Same as above under t)
mean of her students: 86.65
t value from the test above: -.618
Critical t from t-table for 19 df = 2.093
Ours is .62 - which is not that rare
p value (Sig.) from above = .544
So, the test is NOT SIGNIFICANT and we FAIL TO REJECT THE NULL
Fifth graders from her school do NOT differ in their performance from the overall
population mean of 88.
We have no evidence that fifth graders from her school perform better or worse than
5th graders in the population).
*****
II. A researcher wants to test estimates of distance between two poles among 10 students
to see if they differ from the mean estimates of students in the past. In the past, the mean
estimate was 27 feet. Here are the estimates in feet for her 10 students:
Here are 10 estimates: 31, 30, 26, 38, 29, 30, 34, 38, 28, 22
Use SPSS to run a one sample t-test to determine if the students' mean estimate
differs from the estimate of 27 feet in the past.
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HA: μ ≠
H0: μ =
Copy the information from the printout into the following tables:
One-Sample Statistics
N
Mean
Std. Deviation
One-Sample Test
Test Value =
t
df
Sig. (2-tailed)
Mean
Difference
Std. Error
Mean
95% conf.
95% conf.
Lower
Upper
Mean estimate of the 10 students: _____
1. Was the test significant? _________
2. What was the t value in the test above? _________
3. What is the critical t from a t-table? _______
4. Is the test SIGNIFICANT? _____
5. What was the p value (sig.) above? _____
6. Do you REJECT the null hypothesis or FAIL TO REJECT?
_______________________
7. What do you report to the teacher - does it appear that her students estimates are
different from the estimates of students in the past? ___________________
8. If you answered "yes" to #7, tell whether her students' estimates are higher or lower
than past students: ________________________________
***********
III. A researcher is interested in the number of days that successful athletes train to run a
full marathon. She gets the workout logs for one year for all the athletes who completed a
specific marathon in less than four hours. On the average, these athletes of the past
trained for 305 days per year. She is in charge of the training for 20 athletes. After they
run the marathon, she wonders whether their training differed in amount from the training
of successful athletes in the past.
Here are the number of days per year her 20 athletes trained: 230, 220, 214, 300, 310,
299, 200, 240, 305, 288, 297, 215, 199, 233, 255, 280, 303, 277, 280, 299
Use SPSS to run a one sample t-test to determine if the students' mean number of
training days per year differs from the mean of 305 days in the past.
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HA: μ ≠
H0: μ =
Copy the information from the printout into the following tables:
One-Sample Statistics
N
Mean
Std. Deviation
One-Sample Test
Test Value =
t
df
Sig. (2-tailed)
Mean
Difference
Std. Error
Mean
95% conf.
95% conf.
Lower
Upper
Mean number of days training of the 20 athletes: _____
1. Was the test significant? _________
2. What was the t value in the test above? _________
3. What is the critical t from a t-table? _______
4. Is the test SIGNIFICANT? _____
5. What was the p value (sig.) above? _____
6. Do you REJECT the null hypothesis or FAIL TO REJECT?
_______________________
7. What do you report to the trainer - does it appear that her runners trained a different
amount than, students in the past? ___________________
8. If you answered "yes" to #7, tell whether her runners trained more or fewer days than
past athletes: ________________________________
***********
IV. A researcher knows that the mean yearly income of all graduates of a certain college
is $75,000. She wonders how students at her university compares. She gets a random
sample of 15 graduates of her college and determines their yearly income.
Here are the yearly incomes of her sample of 15 graduates: 56000, 164,000, 250,500,
85,000, 95,000, 66,000, 123,000, 42,000, 85,595, 95,230, 55,430, 88,010, 142,000,
105,000, 110,000
Use SPSS to run a one sample t-test to determine if the mean income of graduates of
her college differs from the mean of $75,000 per year for all college graduates. (DO
NOT ENTER COMMAS INTO SPSS DATA.)
HA: μ ≠
H0: μ =
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Copy the information from the printout into the following tables:
One-Sample Statistics
N
Mean
Std. Deviation
One-Sample Test
Test Value =
t
df
Sig. (2-tailed)
Mean
Difference
Std. Error
Mean
95% conf.
95% conf.
Lower
Upper
Mean income of the 15 graduates: _____
1. Was the test significant? _________
2. What was the t value in the test above? _________
3. What is the critical t from a t-table? _______
4. Is the test SIGNIFICANT? _____
5. What was the p value above? _____
6. Do you REJECT the null hypothesis or FAIL TO REJECT?
_______________________
7. What do you report to the professor - does it appear that graduates of her college have
a different income than that of college graduates in the
population?___________________
8. If you answered "yes" to #7, tell whether graduates of her college tend to make MORE
or LESS than college graduates in the population: _______________________________
END