4. Find the biased estimate and unbiased estimate of the population variance for each of the
following samples,
a. n = 12, SS = 2334
b. n = 15, SS = 456
c. n = 25, SS = 1390
5. Find the biased estimate and unbiased estimate of the population variance for each of the
following samples,
a. n = 95, SS = 1964
b. n = 35, SS = 985
c. n = 2, SS = 1776
7. For the following sample sizes, find the degrees of freedom (df) and associated critical values
from the t-distribution.
a. n = 20, p = .05, One-tailed
b. n = 26, p = .01, Two-tailed
c. n = 27, p = .05, One-tailed
d. n = 150, p = .01, Two-tailed
8. The following sample scores were obtained from a population of students.
Score: 4, 5, 6, 7, 8, 10, 11
a. Compute the sample mean, X̄ .
b. Compute the sample variance and standard deviation.
c. Compute the estimated standard error of the mean.
13. To test the effectiveness of a new memory pill that prevents memory loss on adults, a sample
of 35 individuals is selected at random from a normal population of adults known to remember
about μ = 18 words. However, the population variance is unknown. After the treatment is administered, the sample of individuals remember an average of 22 words, with a sample variance
of 16.
a. Using the appropriate notation, define the populations.
b. State the null and research hypotheses.
c. Calculate the estimated standard error of the mean.
d. Calculate the t-score for the sample’s score.
e. Using a p-value of .05, determine whether this memory pill really works.
f. Using a p-value of .01, determine whether this memory pill really works.
g. Were the results statistically significant? Or statistically nonsignificant?
14. To test the effectiveness of note-taking, a sample of 95 high school students is selected at
random from a normal population of high school students with a semester GPA of μ = 76 and an
unknown population variance. The students’ task is to take hand-written notes during class lectures
and during reading and study times. The students’ average GPA for the completion of the semester
is a 79, with a sample variance of 12.
a. Define the populations.
b. State the null and research hypotheses.
c. What is the standard error of the mean?
d. What is the cutoff z-score using a p-value of .01?
e. Calculate the t-score for the first-year student.
f. Did you accept or reject the null hypotheses?