One-sample Tests Practice
1. You have information on a sample of 20 people, and the population standard deviation is known.
Would you use a one-sample z- test or one-sample t-test? Why?
Use t-test with pop standard deviation – in essence same formula, but how you determine the
critical value will be different.
2. How is the standard error of the mean different from standard deviation?
Standard deviation is the average variability from the mean within the sample or pop
Standard Error of the Mean is the standard deviation of all means in the pop
3. Suppose the average BMI for American adult males aged 18-30 is 25. You collected BMI on a
sample of 50 American adult males aged 18-30, and found that the average BMI is 26.5, and the
SEM is 0.375. What is the standard deviation for the population of American adult males?
SEM = σ/√n .375 = σ/√50
SEM (√n) = σ .375(√50) = 2.65
4. The mean for birth weight for all births is 3300 grams with a standard deviation of 750 grams.
We want to know whether birth weights for infants who died of SIDS is significantly different
from that of other infants. In a sample of 36 infants who ultimately died of SIDS, the mean birth
weight is 2890.5 grams, with a standard deviation of 720 grams. Use α = .10.
a. What are the null and research hypotheses?
H0: xbar = 3300
H1: xbar ≠ 3300
b. Construct the 90% confidence interval for birthweight of infants who died from SIDS.
2890.5 +/- 1.645 (720/√36)
2890.5 +/- 197.4
(2693.1, 3087.9)
c. What is the SEM?
d. 750/√36 = 125
e. What would the SEM be if instead of 36 infants, your sample contained 60 infants?
f. 750/√60 = 96.82
g. What is the one-sample z-test test statistic?
(2890.5-3300)/125 = -3.276
h. What is the critical value?
+/- 1.645
i. Is this finding statistically significant? Why or why not?
Yes, obtained value more extreme than critical value. Test statistic is in region of rejection.
j. What is Cohen’s D?
D = |2890.5-3300|/750 = .546
5. The mean class grade for all health sciences statistics students from previous semesters was 85%
with a standard deviation of 7%. We want to know if the current class of statistics students is
significantly different from the previous years’ population. The current mean class grade is 87%
with a standard deviation of 5%. There are 30 students in the class. Use α = .10.
a. What is the SEM?
7/√30 = 1.28
b. What is the critical value?
+/- 1.645
c. What is the one-sample z-test test statistic?
Z = (87-85)/1.28 = 1.56
d. Is this finding statistically significant? Why or why not?
No, obtained value is not as extreme as critical value. Obtained value falls within the region of
nonrejection.
e. What is Cohen’s D?
|87-85|/ 7 = .286
