Witte & Witte, 9e Page 1 of 4 Pages

Chapter 13

Chapter 13: t Test for One Sample

Exercise 1

Use Table B in your textbook to find the critical t values for the following hypothesis tests:

a.  one-tailed test, upper tail critical,  = .01, df = 15

b.  two-tailed test ,  = .05, df = 112

c.  two-tailed test,  = .01, df = 5

d.  one-tailed test, lower tail critical,  = .05, df = 68

Answers:

a.  2.602

b.  ±2.000

c.  ±4.032

d.  -1.671

Exercise 2

Compute degrees of freedom for the t test for one sample for the following sample sizes.

a.  n = 25

b.  n = 80

c.  n = 100

d.  n = 250

Answers:

a.  df = 24

b.  df = 79

c.  df = 99

d.  df = 249

Exercise 3

1. Compute the estimated standard error of the mean for the following situations.

a.  s = 10, n = 25

b.  s = 10, n = 100

c.  s = 48, n = 25

d.  s = 48, n = 100

Answers:

a.  Estimated standard error of the mean = 2

b.  Estimated standard error of the mean = 1

c.  Estimated standard error of the mean = 9.6

d.  Estimated standard error of the mean = 4.8

2.  Look at your answers to problem 1 and present a summary statement regarding the impact of sample size on the magnitude of the standard error of the mean.

Answer:

If the standard deviation is held constant, a larger sample size results in a smaller standard error of the mean.

Exercise 4

1.  Calculate the mean, standard deviation, and standard error of the mean for the following data which represent paid vacation days taken by individuals from nine different countries. Source: http://www.infoplease.com/ipa/A0922052.html.

Country / Days
Italy / 42
France / 37
Germany / 35
Brazil / 34
United Kingdom / 28
Canada / 26
Korea / 25
Japan / 25
U.S. / 13

Answers:

Mean = 29.4444; Standard deviation = 8.5894; Standard error = 2.8631

2.  Use the data in problem 1 to test the hypothesis that the population mean number of vacation days in the industrialized countries of the world is equal to 25. Set alpha equal to .05 for a two-tailed test.

a.  Using symbols, present the null hypothesis.

b.  Using symbols, present the alternative hypothesis.

c.  Calculate df.

d.  Use Table B to find the critical t values.

e.  Calculate observed t.

f.  Present the statistical decision.

g.  Present a summary statement in the context of the research situation.

Answers:

a.  H0:  = 25 days

b.  H1:  ≠ 25 days

c.  df = n – 1 = 9 – 1 = 8

d.  Critical t = ±2.306

e.  Observed t = 1.552

f.  Retain the null hypothesis.

g.  There is no evidence that the population mean number of vacation days differs from 25.

Exercise 5

a.  In a 2008 survey, Americans were asked to name their favorite actor. The most often mentioned living actors are shown below along with their ages in 2008. (John Wayne was number 3 in the list, but we have not included him here because he died in 1979.) One interpretation of the results was that Americans prefer actors older than 30. Do these data support that interpretation? Source: http://www.reuters.com/article/pressRelease/idUS108634+29-Jan-2009+BW20090129

b. 

Actor / Age in 2008
Denzel Washington / 54
Clint Eastwood / 78
Will Smith / 40
Harrison Ford / 66
Julia Roberts / 41
Tom Hanks / 52
Johnny Depp / 45
Angelina Jolie / 33
Morgan Freeman / 71

c.  Calculate the sample mean age.

d.  Calculate the sample standard deviation.

e.  Calculate the standard error of the mean.

f.  Use Table B to identify the critical t value for  = .01 for a two-tailed test.

g.  Construct a 99% confidence interval around the sample mean.

h.  Interpret this confidence interval.

Answers:

a.  Sample mean = 53.333 years

b.  Sample standard deviation = 15.394 years

c.  Standard error = 5.132 years

d.  Critical t = 3.355

e.  99% CI: 53.333 ± 17.219; 99% CI: 36.11 – 70.55 years

f.  We are 99% confident that the interval between 33.11 and 70.55 years includes the true population mean age of Americans’ favorite actors. Since all values of CI exceed 30, it appears that, on average, Americans tend to prefer actors older than 30.

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