Question Type 4: Performing a hypothesis test comparing two means for paired samples Exercises

A study measures screen time (hours) before–after an intervention for 25 subjects. $\bar d=\text{before}-\text{after}=0.5$, $s_d=1.2$. Conduct a two-tailed paired t-test at $\alpha=0.05$.

Fifteen soil samples have pollutant levels before and after treatment. Mean difference (before–after) is $\bar d=3.2$ ppm, $s_d=5.5$ ppm. At $\alpha=0.10$, test if treatment reduces pollution (one-tailed).

Blood pressure of 12 patients is measured before and after drug X. The mean difference (before–after) is $\bar d=-5$ mmHg, with $s_d=6$ mmHg. Conduct a one-tailed paired t-test at the 5% level to see if the drug lowers blood pressure.

Eighteen participants take two recall tests (old, new). The mean difference $d=\text{old}-\text{new}=-1.8$ items, $s_d=2.5$. Test at 5% one-tailed whether the new test yields higher recall (i.e. $\mu_d<0$).

A cognitive researcher measures error counts under two conditions A then B for 16 participants. The mean difference $\bar d=A-B=-2$ errors, with sample standard deviation $s_d=5$. Perform a two-tailed paired t-test at $\alpha=0.05$ to decide if a difference exists.

A coach records sprint times (before, after) for 7 athletes (s): (12.5, 12.1), (12.8, 12.3), (13.0, 12.7), (12.6, 12.4), (12.9, 12.5), (12.7, 12.2), (13.1, 12.9). Test at 5% if training reduces time (paired t-test, one-tailed).

Blood glucose levels are measured before and after a new drug for 30 patients. The mean difference (before–after) is $\bar d=5$ mg/dL with $s_d=9$ mg/dL. At the 1% level, test if the drug lowers glucose (one-tailed).

Reaction times (standard, caffeine) for 10 subjects (s): (0.32, 0.30), (0.28, 0.29), (0.35, 0.33), (0.30, 0.31), (0.33, 0.28), (0.29, 0.30), (0.31, 0.29), (0.34, 0.32), (0.27, 0.25), (0.32, 0.30). Test at 5% one-tailed whether caffeine reduces reaction time.

Eight subjects have their weights recorded before and after a 4-week diet: (85, 82), (90, 88), (78, 75), (110, 105), (95, 93), (100, 98), (72, 70), (88, 85). Test at $\alpha=0.05$ whether the diet leads to weight reduction (one-tailed).

Perform a two-tailed paired t-test at the 5% significance level to determine whether mean calorie consumption differs when watching horror versus romance movies. The calorie consumptions for 10 subjects are (horror, romance): (345, 453), (234, 112), (45, 887), (216, 593), (543, 953), (143, 438), (576, 299), (396, 548), (222, 671), (341, 554).

Using the same data as above, test at the 1% significance level whether mean calorie consumption is higher when watching romance movies than horror movies. Use a one-tailed paired t-test.

In a study of memory, 20 participants learn word lists by method 1 then by method 2. The mean difference in recall (method 2–method 1) is $\bar d=2.5$ points, $s_d=3.1$. Test at 1% significance (two-tailed) whether method 2 differs.