2. Your friend Jane�fs landscaping company charges two hours of labor time for the planting of a medium-sized tree. To make sure she is not undercharging or overcharging for this service, she asks for your help. To start, you take an SRS of 10 planting times from last month�fs landscaping work(times are in hours):
1.7 1.5 2.6 2.2 2.4 2.3 2.6 3.0 1.4 2.3
(a) Compute the sample mean.
(b) Compute the sample standard deviation.
(c) Compute a 95% Confidence Interval for the true mean planting time.
(d) Perform a hypothesis test to see whether the mean tree-planting time differs from 2 hours. Use the Null Hypothesis 𝐻0:𝜇=2.0 and Alternative Hypothesis 𝐻𝑎:𝜇�‚2.0. For the test use a level of significance of 𝛼=0.05.
(e) If you were going to send an email to Jane to communicate your conclusions (assuming she did not take Math 305!), what would you say?
a. mean = sum of scores/number of scores
b. Subtract each of the scores from the mean and square each difference. Find the sum of these squares. Divide that by the number of scores to get variance.
Standard deviation = square root of variance
c. 95% = mean ± 1.96 SD
d. Ho: mean = 2.0
Ha: mean ≠ 2.0
I'll leave the rest to you.