Question

- Suppose that 15 Stata users and 22 Excel users were chosen at
random to conduct a series of statistical analyses. The Stata users
took 20 minutes on average to complete the tests, with a standard
deviation of 5 minutes. The Excel users took 23 minutes on average,
with a standard deviation of 10 minutes. Assume test completion
time in both cases is normally distributed.
- Assume that the standard deviations are known from the
population. At the 10% significance level, prove (or fail to prove)
that a Stata user will complete the tests faster than an Excel user
on average.
- Set up the null and alternative hypotheses.
- Calculate the appropriate test statistic.
- Use either the p-value approach or the critical value approach to reject or fail to reject the null hypothesis.

- Assume that the standard deviations are unknown and are sample deviations computed from the respective samples. Repeat question (a) above under this assumption.
- Assume that we randomly choose 10 analysts and have each perform the tests using Stata and Excel, with the order in which they do the tests being randomly determined, and obtain a difference mean of 4 and a difference sample standard deviation of 7.5. Repeat step (a) above under this assumption.

- Assume that the standard deviations are known from the
population. At the 10% significance level, prove (or fail to prove)
that a Stata user will complete the tests faster than an Excel user
on average.

Answer #1

25 runners and 25 bikers are randomly chosen to do the same
race. The runners took 30 minutes to complete the race on average
and the standard deviation was 5 minutes. The bikers took 35
minutes to complete the race on average and their standard
deviation was 8 minutes. Assume that the race completion times are
normally distributed for both groups.
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16–29 year
olds
30 years old and
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Let x be a random variable that represents hemoglobin
count (HC) in grams per 100 milliliters of whole blood. Then
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14
17
17
18
15
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14
18
15
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Let x be a random variable that represents hemoglobin
count (HC) in grams per 100 milliliters of whole blood. Then
x has a distribution that is approximately normal, with
population mean of about 14 for healthy adult women. Suppose that a
female patient has taken 10 laboratory blood tests during the past
year. The HC data sent to the patient's doctor are as follows.
14
19
15
20
15
12
15
18
16
12
(i) Use a calculator with sample...

Let x be a random variable that represents hemoglobin
count (HC) in grams per 100 milliliters of whole blood. Then
x has a distribution that is approximately normal, with
population mean of about 14 for healthy adult women. Suppose that a
female patient has taken 10 laboratory blood tests during the past
year. The HC data sent to the patient's doctor are as follows.
16
19
17
20
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11
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