Answer:
The confidence interval is (5.2938, 6.8062)
Step-by-step explanation:
Given that:
Standard deviation (σ) = 2.44 words per essay,
Mean (μ) = 6.05,
Confidence interval (c) = 95% = 0.95.
number of students (n) = 40 students
α = 1 - c = 1 - 0.95 = 0.05
[tex]\frac{\alpha }{2} = \frac{0.05}{2} = 0.025[/tex]
From the probability table,[tex]Z_{\frac{\alpha }{2} }=Z_{0.025}=1.96[/tex]
The margin of error (e) is given by the equation:
[tex]e = Z_{\frac{\alpha }{2} }*\frac{\sigma}{\sqrt{n}}[/tex]
Substituting values:
[tex]e = Z_{\frac{\alpha }{2} }*\frac{\sigma}{\sqrt{n}}= 1.96*\frac{2.44}{\sqrt{40} } = 0.7562[/tex]
The confidence interval is given by (μ - e, μ + e).
Therefore: The confidence interval = (μ - e, μ + e) = (6.05 - 0.7562, 6.05 + 0.7562) = (5.2938, 6.8062)
The confidence interval is (5.2938, 6.8062)
