Question

The aim of a study is to investigate whether a new stimulant drug can increase attention and concentration in subjects suffering of ADHD. A group of researchers conduct an experiment where each participant is given a text to read while music is played into the room. The participant is then given a test afterwards on the contents of the text. The score on the test determines focusing skills and higher score implies better concentration on the reading task. A group of 17 participants were administered the stimulant and tested, and a control group of 21 subjects were not given the drug and tested. The results are as follows:

ȳ s n
Stimulant Drug 57.2 10.8 17
Control 44.5 6.2 21

Is there evidence in the data to suggest that the stimulant increases the mean concentration score of more than 10 points? (Take α = 0.01)

Answer 1

To determine if the stimulant increases the mean concentration score by more than 10 points, we will conduct a hypothesis test. We'll use a one-tailed t-test with a significance level of 0.01. Using the given data, you should be able to perform the calculations and determine the results.

Step-by-step explanation:

To determine if there is evidence to suggest that the stimulant increases the mean concentration score by more than 10 points, we will conduct a hypothesis test. Let's denote the mean concentration score for the stimulant group as μstimulant and the mean concentration score for the control group as μcontrol. We'll use a one-tailed t-test with a significance level of α = 0.01.

1. Null Hypothesis (H0): μstimulant - μcontrol ≤ 10

2. Alternative Hypothesis (Ha): μstimulant - μcontrol > 10

3. We'll calculate the t-statistic using the formula: t = (μstimulant - μcontrol) / sqrt(sstimulant2/nstimulant + scontrol2/ncontrol), where sstimulant is the standard deviation of the stimulant group's scores, scontrol is the standard deviation of the control group's scores, nstimulant is the number of participants in the stimulant group, and ncontrol is the number of participants in the control group.

4. We'll compare the t-statistic to the critical value from the t-distribution table with (nstimulant + ncontrol - 2) degrees of freedom and the given significance level. If the t-statistic is greater than the critical value, we'll reject the null hypothesis. Otherwise, we'll fail to reject the null hypothesis.

Using the given data, you should be able to perform the calculations and determine if there is evidence to suggest that the stimulant increases the mean concentration score by more than 10 points.