Question

paired samples t - test example 1
problem
a study was conducted to investigate the effectiveness of hypnotism in reducing pain. results for randomly selected subjects are shown in table 10.14. a lower score indicates less pain. the before value is matched to an after value and the differences are calculated. the differences have a normal distribution. are the sensory measurements, on average, lower after hypnotism? test at a 5% significance level.
subject: a b c d e f g h
before 6.6 6.5 9.0 10.3 11.3 8.1 6.3 11.6
after 6.8 2.4 7.4 8.5 8.1 6.1 3.4 2.0
table 10.14

• write null and alternative hypotheses. is this one or two - tailed test?

Explanation:

Let \( \mu_d=\mu_{\text{before}}-\mu_{\text{after}} \). The null hypothesis \( H_0:\mu_d = 0 \) (no difference in sensory measurements before and after hypnotherapy). The alternative hypothesis \( H_1:\mu_d> 0 \) (sensory measurements are higher before hypnotherapy, so lower after, since \( \mu_d=\mu_{\text{before}}-\mu_{\text{after}}>0 \) implies \( \mu_{\text{before}}>\mu_{\text{after}} \)). This is a one - tailed test because we are specifically testing if \( \mu_d>0 \) (directional claim about the difference).

Answer:

• Null hypothesis: \( H_0:\mu_d = 0 \)
• Alternative hypothesis: \( H_1:\mu_d>0 \)
• This is a one - tailed test.