TI-83 Worksheet Number 28
Statistics – Means: Confidence Intervals and Tests
One Sample T – Confidence Interval
Given the following sample data about automobile speeds in a residential area, find the
90% confidence interval for the true mean speed of the vehicles. Assume that the data
satisfies the necessary conditions so that it can be approximated by a t-distribution.
Speed 29 34 34 28 30 29 38 31 29 34 32
31
31 27 37 29 26 24 34 36 31 34 36
Key Strokes
Stat Enter
29 Enter 34 Enter … 36 Enter
Stat ► ►
8
Enter
2nd L1 Enter
1 Enter
. 9 Enter
Enter
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Comment
Brings up the list editor. Select L1
Enter data in L1
Brings up Tests menu
Selects TInterval
Highlights and selects Data because we have a
list of data. If we knew the sample mean and
the standard deviation for the sample, we would
have selected Stats and inputted these two
items as required.
Enters L1 as List
Enters Freq as 1
Enter .90 for
C-Level
Displays the
confidence
interval, the
sample mean,
standard error,
and sample size
WS 28 Page 1 of 4
One Sample T-Test
Given the sample data above with the assumption that it meets all the conditions to be
approximated by a t-distribution; can you conclude that true mean speed is greater than
30mph? State the hypotheses and find the p-value. Use an alpha value of 5%.
Let  0  30 mph
H 0 :   0
H A :   0
Key Strokes
Stat ► ► 2
Enter
▼ 30 Enter
2nd L1 Enter
1
▼►►
▼ Enter
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Comment
Brings up the Tests menu and selects T- Test
Highlights Data. If we had the sample mean
and the standard error, we would have selected
Stats
Inputs 30 for  0
Inputs L1 for List
Inputs 1 for Freq
Highlights and
selects   0
Displays Results.
Since the p-value
is less than .05,
the alpha level,
the null
hypothesis must
be rejected and
we conclude that the true mean speed is greater
that 30mph.
WS 28 Page 2 of 4
Two Sample T-Interval
We have two brands of batteries, Brand A and Brand B. Following is the data relating to
the working life in minutes for batteries from a sample of both brands.
Brand A 194.0 205.5 199.2 172.4 184.0 169.5
Brand B 190.7 203.5 203.5 206.5 222.5 209.5
Find the 90% confidence interval for the true mean of the difference in the lives of the
batteries:  A   B . Assume the data meets all the necessary conditions so the tdistribution can be used.
Key Strokes
Stat Enter
Stat ► ► 0
Enter
▼ 2nd L1 Enter
2nd L2 Enter
1 Enter 1 Enter
. 9 Enter
Enter
▼ Enter
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Comment
Enter Brand A into L1 and Brand B into L2
Brings up 2-SampTInt command
Highlight and select Data option since we have
the raw data. If we had the mean and standard
deviation for each sample, we would use the
Stats option.
Input L1 as List1
Input L2 as List2
Input 1 for both Freq1 and Freq2
Enter .90 for C-Level
Highlight and
select No for
Pooled. Always
select No for this
option.
Displays the
results. df is the
degrees of
freedom the
calculator used
for the
calculation.
WS 28 Page 3 of 4
Two Sample T-Test
Can we conclude from the data that mean battery life for Brand A is less that the mean
battery life for Brand B? Perform a test. Give the p-value and state your conclusion.
The hypotheses for the test are:
H 0 : 1   2
H A : 1   2
Key Strokes
Stat ► ► 4
Enter
▼ 2nd L1 Enter
2nd L2 Enter
1 Enter 1 Enter
► Enter
▼ Enter
Comment
Selects 2-SampTTest command
Selects and Highlight Data option
Inputs L1 as List1
Inputs L2 as List2
Inputs 1 for both Freq1 and Freq2
Highlights and selects   2
Highlights and
selects No for
Pooled option
▼ ► Enter
Displays the
results
graphically.
Stat ► ► 4 ▼ ▼ ▼ ▼ ▼ ▼ ▼ Enter
Displays the
calculations.
The p-value is
.016. Since the
alpha level is not
given, it is
assumed to be
.05. Since the p-value is less than the alpha
leve, we reject the null hypothesis and conclude
that the mean life of Brand A batteries is less
than the mean life of Brand B batteries.
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WS 28 Page 4 of 4