Answer:
(22.74,24.06) is the required 95% confidence interval for the population mean ACT score of University of Oklahoma students.
Step-by-step explanation:
We are given the following in the question:
Sample size, n = 121
Sample mean = 23.4
Sample standard deviation = 3.65
Level of significance = 0.05
Degree of freedom
[tex]= n - 1 = 120[/tex]
95% Confidence interval:
[tex]\bar{x} \pm t_{critical}\displaystyle\frac{s}{\sqrt{n}}[/tex]
Calculation of critical value:
[tex]t_{critical}\text{ at degree of freedom 120 and}~\alpha_{0.05} = \pm 1.9799[/tex]
Putting the values, we get,
[tex]23.4\pm 1.9799(\dfrac{3.65}{\sqrt{121}} )\\\\ = 23.4 \pm 0.6569\\\\ = (22.7431 ,24.0569)\approx (22.74,24.06)[/tex]
(22.74,24.06) is the required 95% confidence interval for the population mean ACT score of University of Oklahoma students.
