Question

A researcher would like to determine whether an over-the-counter cold medication has an effect on mental alertness. A sample of n= 18 participants is obtained, and each person is given a standard dose of the medication one hour before being tested in a driving simulation task. For the general population, scores on the simulation task are normally distributed with μ = 60. The individuals in the sample had an average score of M = 54 and an s = 8.

Can the researcher conclude that scores on the driving simulation task are significantly different after taking the medication? Use a two-tailed test with α = .05. Be sure to state your null hypothesis, a decision about that null hypothesis, and a conclusion explaining your results with an APA format statement. Calculate Cohen’s d if necessary.

Answer 1

Given that, sample size ( n ) = 18

sample mean ( M ) = 54 and

sample standard deviation ( s ) = 8

significance level $(\alpha)$ = 0.05

The null and the alternative hypotheses are,

$H_0: \mu = 60$

$H_a: \mu \neq 60$

Test statistic is,

$t = \frac { M - \mu}{\frac { s}{\sqrt n }} = \frac { 54-60}{\frac { 8 }{\sqrt { 18}}}= -3.182$

Test statistic is, t = -3.182

t-critical values at $\alpha= 0.05$ with degrees of freedom = n - 1= 18 -1 = 17 are, $t^*= \pm 2.110$

Here, test statiatic = -3.182 < -2.110

so, we reject the null hypothesis ( H₀).

p-value = 0.0055

Conclusion: There is sufficient evidence to conclude that scores on the driving simulation task are significantly different after taking the medication.