Question

Joan’s Nursery specializes in custom-designed landscaping for residential areas. The estimated labor cost associated with a particular landscaping proposal is based on the number of plantings of trees, shrubs, and so on to be used for the project. For cost-estimating purposes, managers use two hours of labor time for planting of a medium-sized tree. Actual times from a random sample of 10 plantings during the past month follow (times in hours) are: 1.7, 1.5, 2.6, 2.2, 2.4, 2.3, 2.6, 3.0, 1.4, 2.3 Which gives a Mean = 2.2 and a standard deviation = 0.516 Using α = 0.10, test whether the population mean tree-planting time differs from two hours

Answer 1

Given that, sample size ( n ) = 10

sample mean = 2.2 and sample standard deviation = 0.516

significance level α = 0.10

The null and the alternative hypotheses are,

Test statistic is,

Since, it is two tailed test, critical values at α = 0.10 with degrees of freedom = 10 - 1 = 9 are, t^* = ± 1.833

Decision rule: reject the null hypothesis if, t < -1.833 or t > 1.833

Here, test statistic = t = 1.226 < 1.833

so, we fail to reject the null hypothesis ( H₀).

Conclusion: there is not sufficient evidence to coclude that the population mean tree-planting time differs from two hours.