Question

answer in the most simplest way and like a teen
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

Short answer: Yes — the new method seems to work. It gives a statistically significant increase in typing speed.

Why (simple steps):
- H0: mean = 60 wpm (old mean). Ha: mean > 60 wpm (we want an increase).
- We can use a z-test because the old-method population standard deviation (σ = 3.5) is given.
- Test statistic: z = (62.57 − 60) / (3.5 / √30) ≈ 4.03.
- That z gives a tiny one-tailed p-value (about 0.00003), way below 0.05.

So we reject H0 and conclude the new method increases words per minute.

Quick caveat: the sample’s own SD (11.45) is much larger than 3.5, which is weird — might mean more variability or some outliers. But with the given σ = 3.5, the result is strongly significant.