Answer:
550 ± 20.789
= [529.211 – 570.789]
Step-by-step explanation:
Before constructing the confidence interval, we would start by calculating the confidence interval
The formula for confidence interval =
μ ± Z × σ/√n
Where
μ = mean
Z = Z score of the confidence interval
σ = Standard Deviation
n = number of the samples
From the question
μ = $550
Z = we are given a 95% confidence interval. The Z score = 1.96
σ = $75
n = 50
Hence,
Confidence interval = μ ± Z × σ/√n
Confidence interval = 550 ± 1.96 × 75/√50
= 550 ± 1.96(10.606601718)
= 550 ±20.789
= [529.211 – 570.789]
Therefore, the 95% confidence interval for the mean annual contribution is
= 550 ± 20.789
= [529.211 – 570.789]
Answer:
The 95% confidence interval of the mean annual contribution, [tex]\bar{x}[/tex] is
$529.21 < [tex]\bar{x}[/tex] < $570.79
Step-by-step explanation:
The parameters given are;
The sample size, n = 50
The mean annual church contribution, [tex]\bar{x}[/tex] = $550
The standard deviation, σ = $75
The confidence level = 95%
The formula for finding the confidence interval having a known mean is given as follows;
[tex]CI=\bar{x}\pm z_{\alpha/2} \times \dfrac{\sigma}{\sqrt{n}}[/tex]
Where, the z value at 95% confidence level = 1.96, we therefore have;
[tex]CI=550 \pm 1.96 \times \dfrac{75}{\sqrt{50}}[/tex]
Which gives the 95% confidence interval of the mean annual contribution, [tex]\bar{x}[/tex], as follows;
$529.21 < [tex]\bar{x}[/tex] < $570.79
