Answer:
[3.75 years, 5.45 years]
Step-by-step explanation:
The 90% confidence interval is given by the interval
[tex]\large [\bar x-t^*\frac{s}{\sqrt n}, \bar x+t^*\frac{s}{\sqrt n}][/tex]
where
[tex]\large \bar x[/tex] is the sample mean
s is the sample standard deviation
n is the sample size
[tex]\large t^*[/tex] is the 0.05 (5%) both-sided (**) critical value for the Student's t-distribution with 19 degrees of freedom (sample size -1), which is an approximation to the Normal distribution for small samples (n≤ 30).
Either by using a table or the computer, we find
[tex]\large t^*= 1.729[/tex]
and our 90% confidence interval is
[tex]\large [4.6-1.729*\frac{2.2}{\sqrt{20}}, 4.6+1.729*\frac{2.2}{\sqrt{20}}]=\boxed{[3.75,5.45]}[/tex]
(**) 5% of the area to the left of [tex]\large -t^*[/tex] and 5% to right of [tex]\large t^*[/tex] for a total of 90% inside the interval [tex]\large [-t^*,+t^*][/tex]
