Respuesta :
Answer:
There is enough evidence to support the claim that the average number of sheets recycled per bin was more than 59.3 sheets.
Step-by-step explanation:
We are given the following in the question:
Population mean, μ = 59.3
Sample mean, [tex]\bar{x}[/tex] = 62.4
Sample size, n = 79
Alpha, α = 0.05
Sample standard deviation, s = 9.86
First, we design the null and the alternate hypothesis
[tex]H_{0}: \mu = 59.3\text{ sheets}\\H_A: \mu > 59.3\text{ sheets}[/tex]
We use one-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{62.4 - 59.3}{\frac{9.86}{\sqrt{79}} } = 2.7945[/tex]
Degree of freedom = n - 1 = 78
Now, [tex]t_{critical} \text{ at 0.05 level of significance, 78 degree of freedom } = 1.6646[/tex]
Since,
[tex]t_{stat} > t_{critical}[/tex]
We fail to accept the null hypothesis and reject it. We accept the alternate hypothesis.
Conclusion:
Thus, there is enough evidence to support the claim that the average number of sheets recycled per bin was more than 59.3 sheets.
