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Section 11.3 HW Questions and Answers
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Section 11.3 HW Questions and Answers Assume that both populations are normally distributed. ​(a) Test whether μ1≠μ2 at the α=0.05 level of significance for the given sample data. ​(b) Construct a 95​% confidence interval about 2μ1−μ2. Population 1: n=16 xbar= 15.5 s= 4.6 ...

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  • November 12, 2024
  • 6
  • 2024/2025
  • Exam (elaborations)
  • Questions & answers

Subjects

  • section 113 hw questions and answers
  • assume that both populations are normally distribu
  • use the given statistics to complete parts a an

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Section 11.3 HW Questions and Answers
Assume that both populations are normally distributed.
(a) Test whether μ1≠μ2 at the α=0.05 level of significance for the given sample data.
(b) Construct a 95% confidence interval about 2μ1−μ2.

Population 1:
n=16
xbar= 15.5
s= 4.6

Population 2:
n=16
xbar= 19.1
s= 3.8 - answer H0: μ1=μ2
H1: μ1≠μ2

p= 0.022

Reject H0, there is
sufficient evidence to conclude that the two populations have different means.

We are 95%
confident that the mean difference is between −6.65 and −0.55.

Use the given statistics to complete parts (a) and (b). Assume that the populations are
normally distributed.
(a) Test whether μ1>μ2 at the α=10.01 level of significance for the given sample data.
(b) Construct a 90% confidence interval about μ1-μ2.

Population 1:
n=29
xbar= 45.5
s= 4.7

Population 2:
n=19
xbar= 42.6
s= 9.9 - answer H0: μ1=μ2
H1: μ1>μ2

t-stat= 1.19
p-value= 0.123

, Do not reject H0.
There is not
sufficient evidence at the α=0.01 level of significance to conclude that μ1>μ2.

The 90%
confidence interval about μ1-μ2 is the range from a lower bound of 1.267
to an upper bound of 7.067.

Test whether μ1<μ2 at the α=0.05
level of significance for the sample data shown in the accompanying table. Assume that
the populations are normally distributed. - answer H0: μ1=μ2
H1: μ1<μ2

p= 0.001

Reject H0. There is
sufficient evidence at the α=0.05 level of significance to conclude that μ1<μ2

A researcher with the Department of Education followed a cohort of students who
graduated from high school in a certain year, monitoring the progress the students
made toward completing a bachelor's degree. One aspect of his research was to
determine whether students who first attended community college took longer to attain a
bachelor's degree than those who immediately attended and remained at a 4-year
institution. The data in the table attached below summarize the results of his study.

a) What is the response variable in this study? What is the explanatory variable?

b) Explain why this study can be analyzed using inference of two sample means.
Determine what qualifications are met to perform the hypothesis test about the
difference between two means. Select all that apply. - answer a) The response
variable is the time to graduate. The explanatory variable is the use of community
college or not.

b) The samples can be reasonably assumed to be random; The samples are
independent; The sample sizes are large (both greater than or equal to 30); The sample
sizes are not more than 5% of the population.

c) Does the evidence suggest that community college transfer students take longer to
attain a bachelor's degree? Use an
alpha equals 0.01α=0.01
level of significance. Perform a hypothesis test. Determine the null and alternative
hypotheses.

d) Construct a 99%
confidence interval for

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