15. 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 trails in which she demonstrates a mean of 116 words with a variance of of 225 words (use 5% level of significance)
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Answers
Answer:
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.
Answer:
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.