Question

A random sample of 121 students from the University of Oklahoma had a sample mean ACT score of 23.4 with a sample standard deviation of 3.65. Construct a 95% confidence interval for the population mean ACT score of University of Oklahoma students.

Answer 1

33

Explanation:

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Answer 2

(22.74,24.06) is the required 95% confidence interval for the population mean ACT score of University of Oklahoma students.

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

`= n - 1 = 120`

95% Confidence interval:

`\bar{x} \pm t_(critical)\displaystyle(s)/(√(n))`

Calculation of critical value:

`t_(critical)\text{ at degree of freedom 120 and}~\alpha_(0.05) = \pm 1.9799`

Putting the values, we get,

`23.4\pm 1.9799((3.65)/(√(121)) )\\\\ = 23.4 \pm 0.6569\\\\ = (22.7431 ,24.0569)\approx (22.74,24.06)`

(22.74,24.06) is the required 95% confidence interval for the population mean ACT score of University of Oklahoma students.