Question

English teacher wants to test whether the mean reading speed of students is 550 words per minute. A sample of 12 students revealed a sample mean of 540 word per minute with a standard deviation of 5 words per minute. At the 0.05 significance level, is the reading speed from 550 words per minute?

Answer 1

$\mu = 550 \\ n=12 \\ \bar{x}=540 \\ s=5 \\ H_0: \mu = 550 \\ H_1: \mu ≠ 550$

When n<30 and $\sigma$ is unknown, a one sample t-test is used.

$t= \frac{\bar{x}- \mu}{s/ \sqrt{n}} \\ t = \frac{540-550}{5 / \sqrt{12}}=-6.93 \\ df=n-1=12-1=11 \\ α=0.05$

Two-tailed test

$t_{α/2,df} = t_{0.025, 11}=2.201$

If test statistics $|t| > t_{α/2,n-1}$ , you have sufficient evidence to reject H₀.

$|t|=6.93 > t_{0.025, 11}=2.201$

Reject H₀.

There is enough evidence to conclude that the mean reading speed of students is NOT 550 words per minute at the 0.05 significance level.