Question 1 (1 point)

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Consider a scenario in
which we decide to compare the price of our textbook on eBay versus in the
University bookstore. For that purpose, we collect 20 observations of sold used
copies of the book on eBay. The average price on eBay is $50. We also compute
the sample standard deviation of $11. The price at the University bookstore is
$75 for a used copy.

Please construct a 95% significance
test for the hypothesis that the average price of the used book on eBay is $75
and state the results of the test here.

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Question 2 (1 point)

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Consider a scenario where you have
two samples. Sample 1 contains 30 observations, has the sample average value of
37 and the sample standard deviation of 2.5. Sample 2 contains 20 observations,
has the sample average of 39 and the sample standard deviation of 2.0.

Based on this information, please
conduct a 90% significance test for the equality of the two population means.
Note that we don’t know the population standard deviations but we can assume
that they are equal.

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Question 3 (1 point)

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Consider a scenario where you have
two samples. Sample 1 contains 30 observations, has the sample average value of
37 and the sample standard deviation of 2.5. Sample 2 contains 20 observations,
has the sample average of 39 and the sample standard deviation of
2.0. Assume that we don’t know the population standard deviations but we
can assume that they are equal.

Which of the following tests would
fail to reject the null hypothesis that the two population means are equal?

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Question 4 (1 point)

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Consider a scenario where you have
two samples. Sample 1 contains 30 observations, has the sample average value of
37 and the sample standard deviation of 2.5. Sample 2 contains 20 observations,
has the sample average of 39 and the sample standard deviation of 2.0. Based on
this information, please conduct a 90% significance test for the hypothesis
that the population mean 2 exceeds the population mean 1 by exactly 3. Please
keep in mind that we don’t know the population standard deviations but can
assume that they are equal.

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Question 5 (1 point)

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Consider a scenario where you have
two samples. Sample 1 contains 30 observations, has the sample average value of
37 and the sample standard deviation of 2.5. Sample 2 contains 20 observations,
has the sample average of 39 and the sample standard deviation of 2.0. Based on
this information, please conduct a 90% significance test for the equality of
the two population means. Note that we don’t know the population standard
deviations AND we can NOT assume that they are equal.

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Question 6 (1 point)

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Consider a scenario where you have two samples. Sample 1
contains 30 observations, has the sample average value of 37 and the sample
standard deviation of 2.5. Sample 2 contains 20 observations, has the sample
average of 39 and the sample standard deviation of 2.0. Based on this
information, please conduct a 90% significance test for the equality of the two
population means and state the degrees of freedom for the test statistic. Note
that we don’t know the population standard deviations AND we can NOT assume
that they are equal.

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Question 7 (1 point)

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Please use the dataset below to conduct a hypothesis test for
the equality of the two population means. Please do so with 95% significance. Also
assume that the two population standard deviations are unknown and cannot be
assumed equal.

Please report the t-test statistic from your test.

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Question 8 (1 point)

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Consider a scenario where you have
two samples. Sample 1 contains 30 observations, has the sample average value of
37 and the sample standard deviation of 2.5. Sample 2 contains 20 observations,
has the sample average of 39 and the sample standard deviation of 2.0. Based on
this information, please conduct a 90% significance test for the equality of
the two population variances.

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Question 9 (1 point)

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Consider the dataset below. It
includes two samples. Please conduct a 90% significance test for the equality
of the two population variances.

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Question 10 (1 point)

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Consider the two samples below and
test for the equality of the two population variances with 95% significance
level and state the results of the test.

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