HP 10413 Datasheet download pdf (Page 153)

153

The test value for the Student-t and the sample mean are listed in the middle

of the screen and the rough position of these values is shown by a vertical

line in both the upper and lower diagrams. The regions for rejection of the

null hypotheses are shown at the very top of the screen by the ‘ R’ and

‘R ’.

We assume, by statistical theory, that the distance

(

)

−

is normally

distributed. If the null hypothesis is true then the mean of this new distribution

should be zero. Our result is indicating that our particular value of

()

− is

of such a size that if the null hypothesis is true then the probability of it

appearing by chance is less than 5%.

In this case, whether you work from the PLOT view or the NUM view, it is clear

from the evidence that the null hypothesis should be rejected, with less than

a 5% chance of this rejection being incorrect. The alternate hypothesis that

the mean is not 50 should be accepted. Of course in this case, despite some

boxes containing less than 50 matches, the actual mean seems to be above

50 so we can hardly condemn the company for putting more matches in the

boxes than they need to!

Confidence interval: T-Int 1-

In the previous example we found that the evidence of our sample indicated

that the mean number of matches in the boxes was not 50. Suppose we now

want to know, at the 95% confidence level, within what range of values the

true population mean lies.

Change back to the SYMB view and

the

method of Conf Interval. The type of interval is

converted to the similar type of T-INT: 1

In the NUM SETUP view use the import facility

as before to import the values from our sample

data. The default confidence level is 99% so

you will need to change that to 0.95.

Changing to the NUM view gives the minimum

and maximum values for the population mean

of 50.16 to 52.44 at a 95% confidence level.

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HP 10413 Datasheet Page 153