Answer
Explanation
For hypothesis testing, the first thing to define is the null and alternative hypothesis.
The null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test.
While, the alternative hypothesis usually confirms the the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the directions of the test.
For this question, since the null hypothesis, H₀, is already given as
H₀: μ = 590
In words, the null hypothesis would be that there is evidence from this sample that the population mean isn't significantly different from 590.
Then, the alternative hypothesis would be that the mean is significantly different from 590. That is,
Hₐ: μ ≠ 590
To know the decision rule, we need to first perform an hypothesis test on this data given
To do this test, we will use the t-distribution because no information on the population standard deviation is known
So, we compute the t-test statistic, which is given as
t = (x - μ)/σₓ
x = sample mean = 595
μ = The standard we are comparing against = 590
σₓ = standard error of the mean = (σ/√n)
σ = sample standard deviation = 8
where n = Sample size = 15
σₓ = (8/√15) = 2.066
t = (x - μ)/σₓ
t = (595 - 590)/2.066
t =