MINITAB Assignment 5
(due Friday May 4)
Confidence Intervals and Hypothesis Tests
< Text (such as this)
which is enclosed in angle brackets, < >,
is communication about what to do in the assignment,
or commentary about it. I will also color such text
green. Text which is not green and bracketed is
text you should type or paste into the session window,
perhaps with obvious changes, such as replacing
Your Name with your name. This will make your
minitab work more meaningful on review and in execution.
Please try to understand the exercise.>
Minitab Assignment 5:
Confidence Intervals and Hypothesis Tests
Your Name
PROBLEM 1: Large Sample Confidence Interval
In this exercise we generate a 95% confidence interval
for the population mean based on some canned data in Minitab.
We use File > Open Worksheet,
then click on the datafile Plating, and open it.
This stores
30 sample numbers from the Plating data file into column C1.
Next we apply
Stat > Basic Statistics > Display descriptive statistics,
click Graphs, click Graphical Summary, ok ok.
This produces a graph, which we print out using
File > Print graph.
< Print out the graph!
It contains numerical statistics in addition
to the pictures. >
The confidence interval produced by Minitab comes from the
following formula:
< In your session window: type in the general formula which
determines the 95% confidence interval Minitab produced
for the mean. Then say what numbers are substituted for the
general terms of your formula. Privately (not in the session
window), check the arithmetic to
be sure you are right. If you get a result which is a little
different than what you expect -- see if you can explain the
difference. >
PROBLEM 2:
Large Sample Hypothesis Test for the Mean
Now we run a hypothesis test on this same plating
data, at level
of significance alpha = .05, for
H_1: mean > 3.0
H_0: mean = 3.0
For this we use
Stat > Basic Stat > 1-sample Z
and in the resulting box put in the information corresponding
to this test: variables C1, test mean 3.0, alternative greather than, type
in st.dev. = 3.042, ok.
< That number 3.042 is the sample standard deviation for this data.
You will get output in your session window. After the output, type your
conclusion
(the data do or do not support alternate hypothesis at this level
alpha =.05);
state the P-value; and in your own words explain
the meaning of the P-value. >
PROBLEM 3:
Small Sample Confidence Interval
We are going to use problem 17 of chapter 9 (see page 390 of the text).
We will get a 95% confidence interval for the density of the earth
(water has density 1) using the
the data given in Problem 17, collected by Henry Cavendish in
1798.
First, we clear C1 entries and then
type into C1 the 23 numbers from that problem 17.
< Doublecheck your typing! Your answer must be correct.>
Then we get your 95% CI with
Stat > Basic Statistics > 1-sample t,
typing C1 in the Variables box, OK.
This confidence interval produced by
Minitab comes from the following formula:
< In your session window: type in the general formula which
determines the 95% confidence interval Minitab produced
for the mean. Then say what numbers are substituted for the
general terms of your formula.
For one of these numbers you will have to use the t-table
in the back of our text. Privately (not in the session
window), check the arithmetic to
be sure you are right. >
PROBLEM 4: Small Sample Hypothesis Test
Still using the data in C1,
we will do a t-test for the claim that
the mean of the earth is not equal to 5. , at
level of significance alpha = .05 .
< Type into the session window the appropriate null hypothesis
H_0 and the appropriate alternate hypothesis H_1.
Then run the test, which
proceeds as the large sample z-test above did,
except that
you choose "1-sample t-test" instead of "1-sample z-test",
you use the not-equal rather than the greater than test,
and you don't have to specify
the standard deviation.
After the output, type your conclusion.
Then state the reported P-value (it should be 0.0000) and
explain the meaning of this P-value.
>