Respuesta :
Answer:
We conclude that mean tree-planting time does not differs from two hours.
Step-by-step explanation:
We are given the following in the question:
1.7, 1.5, 2.6, 2.2, 2.4, 2.3, 2.6, 3, 1.4, 2.3
b) Sample mean
[tex]Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}[/tex]
[tex]Mean =\displaystyle\frac{22}{10} = 2.2[/tex]
c) Sample standard deviation
[tex]\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}[/tex]
where [tex]x_i[/tex] are data points, [tex]\bar{x}[/tex] is the mean and n is the number of observations.
Sum of squares of differences = 2.4
[tex]s= \sqrt{\dfrac{2.4}{9}} = 0.516[/tex]
Population mean, μ = 2 hours
Sample mean, [tex]\bar{x}[/tex] = 2.2 hours
Sample size, n = 10
Alpha, α = 0.05
Sample standard deviation, s = 0.516 hours
a) First, we design the null and the alternate hypothesis
[tex]H_{0}: \mu = 2\text{ hours}\\H_A: \mu \neq 2\text{ hours}[/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{2.2 - 2}{\frac{0.516}{\sqrt{10}} } = 1.2256[/tex]
d) P-value = 0.251453
e) Conclusion:
Since, p value is greater than thee significance level, we fail to reject the null hypothesis and accept it.
Thus, we conclude that mean tree-planting time does not differs from two hours.
