Example A stenographer claims that she can
take dictation at the rate of 120 words per minute. Can we reject
her claim on the basis of 100 trials in which she demonstrated a
mean of 116 words with standard deviation of 15 words ?
Solution: The hypothesis to be tested
is that her claims to be accepted.
In notations Ho : m = 120 and Ha : m ¹ 120
Substituting, = 116, s = 15, n = 100 in
The difference is not significant at both 5% and 1% level of significance i.e. the value of z - score 2.67 is highly significant. Hence Ho is rejected i.e. her claim is to be rejected.
If somebody is interested in the number of trials on the basis of which, with the same figure, her claim would not have been rejected, he can proceed as
i.e. n = 54 trials.
Example An automatic machine was designed
to pack exactly 2 kg. of tea. A sample of 100 packs was examined
to test the machine. The average weight was found to be 1.94 kg.
with standard deviation of 0.10 kg. is the machine working properly
Solution:The null hypothesis to be tested
is that the machine is working properly.
In notations Ho : m
= 2 kg. and Ha : m
Substituting, = 1.94, s = 0.10 , n = 100 in
The z-score is highly significant, hence, we reject Ho on the basis of this sample i.e. the machine is not working properly.