Answer:
This report is valid
Step-by-step explanation:
We use this z score formula to solve for a question where a random number of samples is given:
z-score is z = (x-μ)/σ/√n
where x is the raw score
μ is the population mean
σ is the population standard deviation
n = number of samples
When σ/√n = Standard error
From the above question,
x = $48,574
μ = $48,432
σ = 2000
n = 400 families
z = $48, 574 -$48,432/(2000/√400)
= $48, 574 -$48,432/(2000/20)
= $48, 574 -$48,432/100
= 1.42
The z score is 1.42
H0 = μ = $48,432
At 0.05, we reject H0 if z < - 1.96 or > 1.96
z = 1.42
Therefore, H0 cannot be rejected.
The central limit theorem also holds because a sufficiently large amount of random samples (400) where taken from the population and replaced and this causes the mean to be randomly distributed.
Therefore, from the above z score, what we can conclude about the validity of the report is that the REPORT IS VALID because H0 cannot be rejected and the central limit theorem holds.
