Answer
$t_0\gt -t_α$: null hypothesis is not rejected.
There is not enough evidence to conclude that the mean number of cards per individual is less than 3.5.
Work Step by Step
$H_0:~µ=3.5$ versus $H_1:~µ\lt3.5$
Requirement:
$n\geq30$
$n=160$, so:
$d.f.=n-1=159$
$t_0=\frac{x ̅-µ_0}{\frac{s}{\sqrt n}}=\frac{3.3-3.5}{\frac{2.3}{\sqrt {160}}}=-1.100$
$t_α=t_{0.05}=1.660$
(According to Table VI, for d.f. = 100, the closest value to 159, and area in right tail = 0.05)
Since $t_0\gt -t_α$, we do not reject the null hypothesis.
