Answer:
CI = 28 ± 3.09
Step-by-step explanation:
The sample size, n = 25
The sample mean, m = 28
Standard deviation, s = 7.5
Confidence interval is given as:
CI = Sample mean ± margin of error
We want to find 95% confidence level:
First, let us find the margin of error:
Margin of error = Critical value * standard error
To find the critical value, we need some parameters:
Standard error = [tex]s / \sqrt{n}[/tex]
=> [tex]SE = 7.5 / \sqrt{25}= 7.5 = 5 = 1.5[/tex]
The alpha value, ∝ = 1 - (confidence level / 100) = 1 - 95/100 = 1 - 0.95 = 0.05
Critical probability, p, is given as:
p = 1 - ∝/2 = 1 - 0.05/2 = 1 - 0.025 = 0.975
Now we need the degree of freedom:
df = n - 1 = 25 - 1 = 24
Therefore, the critical value is 2.06 (you can use an online t value calculator).
=> Margin of error = 2.06 * 1.5 = 3.09
Therefore, the confidence interval for the population mean is:
CI = 28 ± 3.09
