The 90% confidence interval = 48.603 < μ < 55.397
Explanation:
Given:
Mean = 52
Standard deviation = 14.6
Sample size, n = 50
Confidence Interval, c = 90%
c = 0.9
Significance level, α = 1 - c
= 1 - 0.9
= 0.1
Critical value, z(α/2) = z(0.05) = 1.645
Critical value = ± 1.645
Margin of error, E = [tex]z(\alpha /2) X \frac{SD}{\sqrt{n} }[/tex]
[tex]=1.645 X\frac{14.6}{\sqrt{50} } \\\\= 3.3965[/tex]
Limits of 90% confidence interval are given by:
Lower limit = μ - E
= 52 - 3.397
= 48.603
Upper limit = μ + E
= 52 + 3.397
= 55.397
Thus, 90% confidence interval = 48.603 < μ < 55.397
