Respuesta :
Answer:
The average of minicomputers is not 7.2 days of downtime per year.
Step-by-step explanation:
We are given the following in the question:
Population mean, μ = 7.2 days
Sample mean, [tex]\bar{x}[/tex] = 4.4 days
Sample size, n = 7
Alpha, α = 0.01
Sample standard deviation, s = 1.1 days
First, we design the null and the alternate hypothesis
[tex]H_{0}: \mu = 7.2\text{ days of downtime per year}\\H_A: \mu \neq 7.2\text{ days of downtime per year}[/tex]
We use two-tailed 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{4.4 - 7.2}{\frac{1.1}{\sqrt{7}} } = -6.734[/tex]
Now,
[tex]t_{critical} \text{ at 0.01 level of significance, 6 degree of freedom } = \pm 3.707[/tex]
Since,
Since, the calculated t-statistic does not lie in the acceptance region, we fail to accept the null hypothesis and reject it. We accept the alternate hypothesis.
Conclusion:
Thus, we conclude there is not enough evidence to support the claim that minicomputers actually average 7.2 days of downtime in the entire population.
