FIGURE 23. Sampling distribution of the mean.becomes P(1.841 < /x < 1.871) = 0.95. Thus, there is a 95 percent probability that the
mean length of all rods lies between 1.841 and 1.871 m.
Related Calculations: Note that the confidence interval is a function of the de-
gree of probability that is demanded, and the two quantities vary in the same direction.
For example, if the confidence level were 90 percent, the confidence interval would be
1.844 to 1.868m.
DECISION MAKING ON STATISTICAL BASIS
Units of a commodity are produced individually, and studies have shown that the time re-
quired to produce a unit has a mean value of 3.50 h and a standard deviation of 0.64 h. An
industrial engineer claims that a modification of the production process will substantially
reduce production time. The proposed method was tested on 40 units, and it was found
that the mean production time was 3.37 h per unit. Management has decided that it will
make the proposed modification only if there is a probability of 95 percent or more that
the engineer's claim is valid. What is your recommendation?
Calculation Procedure:
- Formulate the null and alternative hypotheses
The population consists of all units that will be produced under the modified method if it
is adopted, and the sample consists of the 40 units actually produced under this method.
An assumption based on conjecture is termed a hypothesis. A hypothesis that is formulat-
ed merely to provide a basis for investigation is a null hypothesis, and any hypothesis that
contradicts the null hypothesis is an alternative hypothesis. However, interest centers on
the particular alternative hypothesis that is significant in the given case. The null and al-
ternative hypotheses are denoted by Tf 0 and HI , respectively.
Let X= time required to produce 1 unit, h. Place the burden of proof on the industrial
engineer by assuming that production time under the modified method is identical with
Sample mean XCross-hatched area = MStandard deviation = O"x