A Scientist Was Interested in the Success of a Newly $\quad$

A scientist was interested in the success of a newly developed sleep aid called 'Night Owl' on time taken to fall asleep and quality of sleep. She recruited 30 participants who were randomly allocated to receive either a dose of Night Owl or a placebo. The scientist measured the mean time taken for each participant to fall asleep (minutes) and the quality of their sleep (measured on a scale of 1 (poorest quality) to 10 (best possible quality) ) over the course of one week.
-What does the output below show?
$\quad$$\quad$ Box's Test of Equality
$\quad$$\quad$$\quad$ of Covariance
$\quad$$\quad$$\quad$$\quad$ Matrices ${ } ^ { a }$
$\begin{array}{|l|r|}\hline \text { Box's M } & .229 \\\text { F } & .070 \\\text { df1 } & 3 \\\text { df2 } & 141120.000 \\\text { Sig. } & .976\\\hline\end{array}$
Tests the null hypothesis that the observed covariance matrices of the dependent variables are equal across groups.

a. Design:
Intercept + Drug Bartlett's Test of Sphericity ${ } ^ { a }$
$\begin{array}{|l|r|}\hline \text { Likelihood Ratio } & .000 \\\text { Approx. Chi-Square } & 101.046 \\\text { df } & 2 \\\text { Sig. } & .000\\\hline\end{array}$

Tests the null hypothesis that the residual covariance matrix is proportional to an identity matrix.
a. Design: Intercept + Drug

A) The assumption of equality of covariance matrices has been violated.
B) The assumption of sphericity has been met.
C) The covariance matrices are not significantly equal.
D) The covariance matrices are roughly equal as assumed.