Answer:
96% confidence interval for desired retirement age of all college students is [54.30 , 55.70].
Step-by-step explanation:
We are given that a survey was conducted to determine the average age at which college seniors hope to retire in a simple random sample of 101 seniors, 55 was the average desired retirement age, with a standard deviation of 3.4 years.
Firstly, the Pivotal quantity for 96% confidence interval for the population mean is given by;
P.Q. = ~
where, = sample average desired retirement age = 55 years
= sample standard deviation = 3.4 years
n = sample of seniors = 101
= true mean retirement age of all college students
<em>Here for constructing 96% confidence interval we have used One-sample t test statistics as we don't know about population standard deviation.</em>
<u>So, 96% confidence interval for the population mean, </u><u> is ;</u>
P(-2.114 < < 2.114) = 0.96 {As the critical value of t at 100 degree
of freedom are -2.114 & 2.114 with P = 2%}
P(-2.114 < < 2.114) = 0.96
P( <
<
) = 0.96
P( <
<
) = 0.96
<u>96% confidence interval for</u> = [
,
]
= [ ,
]
= [54.30 , 55.70]
Therefore, 96% confidence interval for desired retirement age of all college students is [54.30 , 55.70].