Respuesta :
Answer:
We conclude that the mean number of residents in the retirement community household is less than 3.36 persons.
Step-by-step explanation:
We are given the following in the question:
Population mean, μ = 3.36
Sample mean, [tex]\bar{x}[/tex] = 2.71
Sample size, n = 25
Alpha, α = 0.10
Sample standard deviation, s = 1.10
First, we design the null and the alternate hypothesis
[tex]H_{0}: \mu = 3.36\text{ residents per household}\\H_A: \mu < 3.36\text{ residents per household}[/tex]
We use One-tailed(left) t test to perform this hypothesis.
Formula:
[tex]t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }[/tex] Putting all the values, we have
[tex]t_{stat} = \displaystyle\frac{2.71 - 3.36}{\frac{1.10}{\sqrt{25}} } = -2.95[/tex]
Now, [tex]t_{critical} \text{ at 0.10 level of significance, 24 degree of freedom } =-1.31[/tex]
Since,
[tex]t_{stat} < t_{critical}[/tex]
We reject the null hypothesis and fail to accept it.
Thus, we conclude that the mean number of residents in the retirement community household is less than 3.36 persons.
