Answer:
95% confidence interval for the mean credit hours taken by a student each quarter is [14.915 hours , 15.485 hours].
Step-by-step explanation:
We are given that a random sample of 250 students at a university finds that these students take a mean of 15.2 credit hours per quarter with a standard deviation of 2.3 credit hours.
Firstly, the pivotal quantity for 95% confidence interval for the population mean is given by;
P.Q. = ~
where, = sample credit hours per quarter = 15.2 credit hours
s = sample standard deviation = 2.3 credit hours
n = sample of students = 250
= population mean credit hours per quarter
<em>Here for constructing 95% confidence interval we have used One-sample t test statistics as we know don't about population standard deviation.</em>
So, 95% confidence interval for the population mean, is ;
P(-1.96 < < 1.96) = 0.95 {As the critical value of t at 249 degree of
freedom are -1.96 & 1.96 with P = 2.5%}
P(-1.96 < < 1.96) = 0.95
P( <
<
) = 0.95
P( <
<
) = 0.95
<u><em>95% confidence interval for</em></u> = [
,
]
= [ ,
]
= [14.915 hours , 15.485 hours]
Therefore, 95% confidence interval for the mean credit hours taken by a student each quarter is [14.915 hours , 15.485 hours].
<em>The interpretation of the above confidence interval is that we are 95% confident that the true mean credit hours taken by a student each quarter will be between 14.915 credit hours and 15.485 credit hours.</em>