95% confidence intervals

[Trond]

I just came up with this, after flipping through tables and books to do each stage of the confidence intervals. What do you think?

HP 67 Program: 95% Confidence intervals, one variable:
Assumes normal distribution. I have obtained the coefficients from classic statistics literature on t-distributions and normal distributions.

Collect data (one variable) with ∑+.
Run A for 95% confidence interval of a sample size n=5; B n=10; C n=15; D n=20; E n=30 or above
(E is exact at 60 but a good estimate; for other samples you can also try the next lower and higher value for an idea)

The program puts the +/- value around the mean in in the X register and in variable Reg.1, the lower limit of the interval in R2,
the upper limit of the interval in R3, number of data n in RA, the mean in RB (and Y register), the standard deviation in RC, and Student t value in RD



LBL A
2
.
7
7
6
STO D
GSB 1
RTN

LBL B
2
.
2
6
2
STO D
GSB 1
RTN

LBL C
2
.
1
4
5
STO D
GSB 1
RTN

LBL D
2
.
0
9
3
STO D
GSB 1
RTN

LBL E
2
STO D
GSB 1
RTN

LBL 1
P<>S
RCL 9
P<>S
STO A
Mean X
STO B
Stdv
STO C
RCL A
SQRT
/
RCL D
x
STO 1
RCL B
+
STO 3
RCL B
RCL 1
-
STO 2
RCL B
RCL 1
RTN


Example:
What is the mean weight of adult blue whales in the wild, with a 95% confidence interval, assuming normal distribution?
Say that we have the following sample of weights in metric tons from old whaling records:
90, 176.5, 95, 60, 92, 80, 100, 120, 62, 98
Collect data with ∑+
Run B: the +/- value is in the x register and the mean in the Y register : 97.35 tons +/- 23.63, or check by RCL 2 and RCL 3 (73.72-120.98 tons)

[PedroLeiva]

Very nice, congratulations. Pedro

[Trond]

(05-07-2020 12:00 PM)PedroLeiva Wrote:  Very nice, congratulations. Pedro

Thank you!
I'll see if I can make a program for any value of n later (but t-values are complicated)

[SlideRule]

Are you familiar with the HP-25 program Mean, Std. Deviation, 90/95% Confidence Intervals, Mean ± CI (APol-18; pgs. 95-99), in HP-25 PROGRAMMABLE POCKET CALCULATOR APPLIED TO AIR POLLUTION MEASUREMENT STUDIES: STATIONARY SOURCES, in the General Software Library? Although the title reflects poorly on the depth & breadth of the subject matter, the contents (especially APol-18) may prove useful in your endeavors.

BEST!
SlideRule

[Trond]

(05-08-2020 11:57 PM)SlideRule Wrote:  Are you familiar with the HP-25 program Mean, Std. Deviation, 90/95% Confidence Intervals, Mean ± CI (APol-18; pgs. 95-99), in HP-25 PROGRAMMABLE POCKET CALCULATOR APPLIED TO AIR POLLUTION MEASUREMENT STUDIES: STATIONARY SOURCES, in the General Software Library? Although the title poorly reflects on the depth & breadth of the subject matter, the contents (especially APol-18) may prove useful in your endeavors.

BEST!
SlideRule

Thanks for the info!

EDIT: link does not seem to work. Do you have another link?

[SlideRule]

Yes! Same location, different 'entry'. The original post is updated w/ 'new' link - sorry for any confusion - seems that links from a well-used search engine are site / time / etc. / SPECIFIC. This link is from a cached site, thanks for the heads-up.

BEST!
SlideRule

ps: try HP-25 PROGRAMMABLE POCKET CALCULATOR APPLIED TO AIR POLLUTION MEASUREMENT STUDIES: STATIONARY SOURCES then use the Adobe PDF icon on the right to download.

[PedroLeiva]

Great finding SlideRule, very interesting. You are right, titles does not reflect the real content. Pedro

[SlideRule]

A working link for the HP-65 version of the text: HP-65 PROGRAMMABLE POCKET CALCULATOR APPLIED TO AIR POLLUTION MEASUREMENT STUDIES: STATIONARY SOURCES

the original post (HP-65) Air Pollution Measurement Studies: Stationary Sources is also 'updated'.

BEST!
SlideRule

[PedroLeiva]

Right, the infoemation about confidense interval is in pg68 of the book, or pg75 in PDF. I check that you are always attentive. Pedro