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,
H0: µ = 3
For the alternative hypothesis,
H1: µ > 3
This is a right tailed test.
Since the population standard deviation is not given, the distribution is a student's t.
Since n = 100
Degrees of freedom, df = n - 1 = 100 - 1 = 99
t = (x - µ)/(s/√n)
Where
x = sample mean = 3.1
µ = population mean = 3
s = samples standard deviation = 0.5
n = number of samples = 100
t = (3.1 - 3)/(0.5/√100) = 2
We would determine the p value using the t test calculator. It becomes
p = 0.024
Alpha = 1 - confidence level = 1 - 0.95 = 0.05
Since alpha, 0.05 > than the p value, 0.024, then we would reject the null hypothesis. Therefore, at 95% confidence level, it can be concluded that the mean of the population is significantly greater than 3.
