Answer:
Step-by-step explanation:
We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean
For the null hypothesis,
µ = 16.4
For the alternative hypothesis,
µ ≠ 16.4
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 = 16.4
x = 17.1
σ = 3.1 feet
n = 31
z = (17.1 - 16.4)/(3.1/√31) = 0.89
The calculated test statistic is 0.89 for the right tail and - 0.89 for the left tail
Since α = 0.01, the critical value is determined from the normal distribution table.
For the left, α/2 = 0.01/2 = 0.005
The z score for an area to the left of 0.005 is - 2.575
For the right, α/2 = 1 - 0.005 = 0.995
The z score for an area to the right of 0.995 is 2.575
In order to reject the null hypothesis, the test statistic must be smaller than - 2.575 or greater than 2.575
Since - 0.89 > - 2.575 and 0.89 < 2.575, we would fail to reject the null hypothesis.
Therefore, this information does not suggest that the storm is (perhaps temporarily) increasing above the severe rating
