Question

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A keyboarding instructor wants to test if a new method of instruction is ​effective.
​
​With the old method students typed a mean of 60
words per ​minute with a standard deviation of 3.5
words per minute.
​
​Thirty students ​selected at random received instruction using the new method and were ​then given a typing test.
​
​The mean and standard deviation of the typing ​speeds of the 30
students was approximately 62.57
and 11.45
, respectively.
​
​Would you conclude the new method of instruction is effective in increasing ​the number of words per minute?
​
​Explain your answer.

Answer 1

Simple answer:

- Hypotheses: H0: μ = 60 (no increase) vs Ha: μ > 60 (increase).
- Use a one-sample t-test because the new-method population SD is unknown.
t = (62.57 − 60) / (11.45 / √30) = 2.57 / 2.09 ≈ 1.23 (df = 29).
- One-tailed p ≈ 0.11 (> 0.05), so do not reject H0.

Conclusion: There is not enough evidence (at the 5% level) to conclude the new method increases words per minute.

(If you incorrectly treat the old-method SD = 3.5 as the known population SD, you get z ≈ 4.02 and a significant result — but that is not the appropriate test here because the new-method SD is unknown and we should use the sample SD.)