Asked by c
A keyboarding instructor wants to test if a new method of instruction is effective.
With the old method students typed a mean of
words per minute with a standard deviation of
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
students was approximately
and
, respectively.
Would you conclude the new method of instruction is effective in increasing the number of words per minute?
Explain your answer.
All Answers 1
Answered by
GPT-5 mini
AI
I can help, but the problem statement you posted is missing the numeric values (old-method mean and SD, and the new-sample mean and SD). Please supply those four numbers and the significance level you want to use (if you have one; otherwise I’ll use α = 0.05).
In the meantime, here are the exact steps and formulas I will use once you give the numbers:
1. State hypotheses (one-sided test because you want to know if speed increased):
- H0: μ = μ0 (mean typing speed with new method equals the old-method mean μ0)
- Ha: μ > μ0 (new method increases mean words per minute)
2. Choose α (commonly 0.05).
3. Test statistic (use a one-sample t-test unless the population SD is known):
- t = (x̄ − μ0) / (s / sqrt(n))
where x̄ = sample mean, s = sample standard deviation, n = sample size (here n = 30).
- Degrees of freedom = n − 1.
4. Decision rule:
- Find the critical t value t_{α, n−1} for a one-sided test, or compute the p-value = P(T_{n−1} ≥ t).
- If t > t_{critical} (or p-value < α) reject H0 and conclude the new method is effective.
- Otherwise do not reject H0.
5. Report result: give the t statistic, degrees of freedom, p-value, and a plain-language conclusion. Optionally give a (1 − α)·100% one-sided confidence bound for μ (or a two-sided CI for the difference).
6. Assumptions to check:
- Sample is random (stated).
- Data are approximately normally distributed or n is large enough (n = 30 is borderline but usually acceptable).
- If the old-method SD was stated as a population σ (known), you could instead use a z-test; otherwise use the t-test.
If you give me the old-method mean and SD, the sample mean and SD, and α (or let me use 0.05), I will compute the t statistic and p-value and give the conclusion.
In the meantime, here are the exact steps and formulas I will use once you give the numbers:
1. State hypotheses (one-sided test because you want to know if speed increased):
- H0: μ = μ0 (mean typing speed with new method equals the old-method mean μ0)
- Ha: μ > μ0 (new method increases mean words per minute)
2. Choose α (commonly 0.05).
3. Test statistic (use a one-sample t-test unless the population SD is known):
- t = (x̄ − μ0) / (s / sqrt(n))
where x̄ = sample mean, s = sample standard deviation, n = sample size (here n = 30).
- Degrees of freedom = n − 1.
4. Decision rule:
- Find the critical t value t_{α, n−1} for a one-sided test, or compute the p-value = P(T_{n−1} ≥ t).
- If t > t_{critical} (or p-value < α) reject H0 and conclude the new method is effective.
- Otherwise do not reject H0.
5. Report result: give the t statistic, degrees of freedom, p-value, and a plain-language conclusion. Optionally give a (1 − α)·100% one-sided confidence bound for μ (or a two-sided CI for the difference).
6. Assumptions to check:
- Sample is random (stated).
- Data are approximately normally distributed or n is large enough (n = 30 is borderline but usually acceptable).
- If the old-method SD was stated as a population σ (known), you could instead use a z-test; otherwise use the t-test.
If you give me the old-method mean and SD, the sample mean and SD, and α (or let me use 0.05), I will compute the t statistic and p-value and give the conclusion.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.