Answer:
Step-by-step explanation:
a) We would set up the hypothesis test.
For the null hypothesis,
H:0 µ = 280000
For the alternative hypothesis,
H1: µ ≠ 280000
This is a 2 tailed test
Since the population standard deviation is given, z score would be determined from the normal distribution table. The formula is
z = (x - µ)/(σ/√n)
Where
x = sample mean
µ = population mean
σ = population standard deviation
n = number of samples
From the information given,
µ = 280000
x = 294365
σ = 22898
n = 36
z = (294365 - 280000)/(22898/√36) = 3.76
b) Since α = 0.05, the critical value is determined from the normal distribution table.
For the left, α/2 = 0.05/2 = 0.025
The z score for an area to the left of 0.025 is - 1.96
For the right, α/2 = 1 - 0.025 = 0.975
The z score for an area to the right of 0.975 is 1.96
In order to reject the null hypothesis, the test statistic must be smaller than - 1.96 or greater than 1.96
Therefore, the rejection regions are area to the left of - 1.96 and to the right of 1.96 on the normal distribution curve.
The calculated test statistic is 3.76 for the right tail and - 3.76 for the left tail
c) Since - 3.76 < - 1.96 and 3.76 > 1.96, we would reject the null hypothesis.
