Question

Attention deficit hyperactivity disorder (ADHD) in young
children presents significant challenges to the children, their
parents, and their classroom teachers. Stimulant medication can
effectively treat 60% to 70% of youth with ADHD. Yet many parents
seek alternative therapies, and Hypericum perforatum (St John's
wort) is 1 of the top 3 alternative therapies used.

In a recent study in the Journal of the American Medical
Association, *Hypericum perforatum (St John's Wort) for
Attention-Deficit/Hyperactivity Disorder in Children and
Adolescents, 2008;299(22):2633-2641*, the authors conducted a
randomized, double-blind, placebo-controlled trial to determine the
efficacy and safety of St. John's wort for the treatment of ADHD in
children.

After careful pre-screening, 54 children were randomly assigned
to two treatment groups; 27 children were assigned to receive a
placebo treatment and 27 children were assigned to receive a
treatment with St. John's wort.

A measure of "inattentiveness" was used to evaluate the effect of the treatments. At the beginning of the experiment, the placebo group and treatment group had the same inattentiveness score. After 4 weeks of the experiment, the data in the table below were obtained (a lower inattentiveness score indicates a longer attention span):

Placebo Group |
St. John's Wort Group |

x_{1} = 14.0 |
x_{2} = 13.4 |

s = 3.87_{1} |
s = 3.22_{2} |

n = 27_{1} |
n = 27_{2} |

**Question 1**. Calculate a 99% confidence interval
for the difference *μ*_{1} - *μ*_{2},
where *μ*_{1} is the mean inattentiveness score
after 4 weeks for all ADHD children who receive a placebo, and
*μ*_{2} is the mean inattentiveness score after 4
weeks for all ADHD children who receive St. John's wort.

lower bound of interval

upper bound of interval

**Question 2**.Select the choice below that
correctly interprets the interval in question 1.

I am 99% confident that the average change of the
inattentiveness score for children in this study is in the
interval.I am 99% confident that the interval in question 1
captures the true mean difference *μ*_{1} -
*μ*_{2}; based on this interval it does not appear
that St. John's wort is an effective treatment for
ADHD. I am 99% confident that if a child
with ADHD is given St John's wort, the child's inattentiveness
score will change by an amount in the interval.If St. John's wort
is tested on another sample of ADHD children, there is a 99% chance
that their average inattentiveness score will change by an amount
in the interval.The inattentiveness score of 99% of the children
studied changed by an amount in the interval.The probability that
*μ*_{1} - *μ*_{2} is in the interval
is 0.99.

Answer #1

1)

Placebo Group |
St. John's Wort Group |

x1 = 14.0 |
x2 = 13.4 |

s1 = 3.87 |
s2 = 3.22 |

n1 = 27 |
n2 = 27 |

99% CI

alpha = 0.01, df = 52

CI | Unequal variance | |

tc | 2.673733631 | T.INV.2T(alpha,df) |

Upper | 3.19050822 | (X1 bar-X2 bar )+tc*SQRT(S1^2/n1 + S2^2/n2) |

Lower | -1.99050822 | (X1 bar-X2 bar )-tc*SQRT(S1^2/n1 + S2^2/n2) |

CI = (-1.9905, 3.1905)

2)

We are 99% confident that true population mean difference is lie between this confidence interval

I am 99% confident that the average change of the inattentiveness score for children in this study is in the interval

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