Question

1. Joan’s Nursery specializes in custom-designed landscaping for residential areas. The estimated labor cost associated with a particular proposal is based on the number of planting of trees, shrubs and so on to be used for the project. For cost estimating purposes, managers use two hours of labor time for the planting of a medium-sized tree. Previous studies showed that the population standard deviation of the labor time for plantings is 0.4 hour. Actual times from a sample of 14 plantings during the past months follow (times in hours).

1.8    1.5    2.4    2.2    1.7    1.9    2.1    2.3    1.8    2.4    2.5    2.2    1.8    1.9

1. (6 pts.) Use the classical approach or the p-value approach to determine if the mean tree-planting time differs from two hours.
2. (2 pts.) Suppose that you would like to estimate the mean tree-planting time within 15 minutes with 99% confidence. What sample size should be used?

Answer 1

a)The mean for the given sample is calculated using

Hence Mean=1.96

and standard deviation is given as

s=0.4

The hypotheses are:

rejection region:

reject Ho if |T_obs|>t_0.005,13=3.01

Test statistic:

P-value :

P-value is calculated using T statistic at Degree of freedom=n-1=14-1=13

0.5<P-value<1.0

Conclusion:

Since the |T_obs|<t_0.005,13=3.01 and P-value >0.01 (level of significance assumed as 0.01) we fail to reject the null hypothesis and conclude that there is insufficient evidence to support the claim.

b) If level of significance is 0.01 hence Z =2.58

minimum sample value

Here E=0.25 hrs

So by calculation