University of Minnesota, Twin Cities
School of Statistics
Stat 3011
Rweb
Textbook (Wild and Seber)
Stat 3011 (Geyer) Second Midterm (Computer Lab Part)
Go to question:
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General Instructions
The exam is open book, open web pages. You may use the computer,
a calculator, or pencil and paper to get answers, but it is expected
that you will use the computer. Show all your work:
- For simple computer commands, you may just write the command
you used and the result it gave on this test form.
- For complicated commands or plots, make a printout and attach
the printout to the test form (we'll provide a stapler).
No credit for numbers with no indication of where
they came from!
Suppose a random variable T has Student's t distribution
with 5 degrees of freedom.
- Find the probability that T is less than -5.0.
- Find the probability that T is greater than 1.5.
- Find the probability that T is greater than 2.0 in absolute
value, that is, pr(|T| > 2.0).
- Find the t such that pr(|T| > t) = 0.10.
Two groups of students in physics lab repeatedly measured the measured
voltage on a battery using a voltmeter. Each group had a different battery.
Each group did four measurements. Their measurements are typed in the
Rweb form below as the vectors x and y respectively.
- Find a 99% confidence interval (note: not 95%) for the difference of
the true voltages of the batteries measured by the two groups.
- What assumptions are needed about the probability distributions of
battery measurements in order for interval to actually have its stated
confidence level?
You may use the form below to answer this question.
The task in this question is to calculate real two standard error (2 s. e.)
intervals for the questions done the quick and dirty
way yesterday.
First the data.
In poll about dessert preferences, some questions and answers were
| | yes | no
| don't know or not sure
|
|---|
| Generally eat dessert | 71% | 21% | 8%
|
| Like ice cream | 77% | 18% | 5%
|
| Like vanilla ice cream | 68% | 20% | 12%
|
For the subgroup consisting of children under 10 years of age the answers were
| | yes | no
| don't know or not sure
|
|---|
| Generally eat dessert | 91% | 3% | 6%
|
| Like ice cream | 95% | 5% | 0%
|
| Like vanilla ice cream | 80% | 12% | 8%
|
The sample size for the whole poll was 1067. The number of children
under 10 years of age in the poll was 67.
- What is the 2 s. e. interval for the 71% eating dessert
in the whole sample?
- What is the 2 s. e. interval for the 91% eating dessert
in the children under 10?
- What is the 2 s. e. interval for the difference
77% - 68% = 9% in preference between ice cream in general and vanilla
ice cream in the whole sample?
- What is the 2 s. e. interval for the difference
95% - 80% = 15% in preference between ice cream in general and vanilla
ice cream in the children under 10?