Question

An advertisement for a​ speed-reading course claimed that the​ "average" reading speed for people completing the course was 1000 words per minute. Shown below are the actual data for the reading speeds per minute for a sample of 24 people who completed the course. Complete parts​ (a) through​ (c) below.
1000
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650
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Answer 1

First compute sample summary statistics.

Data (n = 24) sum = 20,500 so
- sample mean x̄ = 20,500 / 24 = 854.17 words/min (rounded)
- sample standard deviation s ≈ 157.38 words/min

(a) Set up hypotheses
- H0: μ = 1000 (the advertised average)
- Ha: μ ≠ 1000 (two‑tailed)

(b) t test
- Test statistic: t = (x̄ − 1000) / (s/√n)
= (854.17 − 1000) / (157.38/√24)
≈ −145.83 / 32.12 ≈ −4.54
- Degrees of freedom = 23.
- p-value (two‑tailed) is very small (p < 0.001).

Conclusion: Reject H0. The sample provides strong evidence that the true mean reading speed after the course is different from 1000 wpm; the sample mean is substantially lower.

(c) 95% confidence interval for the mean
- t0.025,23 ≈ 2.069
- margin = 2.069*(157.38/√24) ≈ 66.46
- 95% CI: 854.17 ± 66.46 ⇒ (≈787.7, 920.6) words/min.

Interpretation: We are 95% confident the true mean reading speed for course completers is between about 788 and 921 wpm — well below the advertised 1000 wpm.

(Assumptions: data are from a random sample or representative group and the t‑procedure is reasonable for n = 24; results are consistent with a clear difference from 1000.)