SOLVING CONFIDENCE INTERVAL FOR Z
Question: What is the 95% confidence interval when the sample mean is 583.578,
standard deviation is 8.764 and a sample size of 500?
Step 1: Determine sample mean and the sample standard deviation.
Sample mean = x
= 583.578 (rounded to three decimal places)
Sample standard deviation = s = 8.764 (rounded to three decimal places)
Step 2: Determine the other given values.
sample size = n = 500
critical value = z =1.96
Explanation: We use z table because the sample size is greater than 30. Furthermore, the level
of significance is 0.05 (5%) because the given confidence level is 95%.
Step 3: Determine the formula to use.
CI =x ± zα/2
(
σ
√
n
)
where;
Cl = confidence Interval
x
= sample mean
z = critical value
σ
= standard deviation
n = sample size
Step 4: Solve
Cl = confidence Interval = unknown
x
= sample mean = 583.578
Z = critical value = 1.96
σ
= standard deviation = 8.764
