Imagine we are taking measurements from the height of mature shrubs. We are interested in seeing whether the shrubs we observe in a particular region differ from those we have observed elsewhere, which we measured as having a median height of 1.65 m. We measure 100 plants and identify that 21 have a height less than 1.65 m (a) What are the hypotheses I would use to test whether the typical height in the region of interest is different to the broader population? (b) If H0 is true, what is the sampling distribution of the number of trees smaller than 1.65 m? (c) Construct a 95% CI for the proportion smaller than the median. (d) Determine the p-value for the same hypotheses, and use this to do a hypothesis test with α = 0.05.
Imagine we are taking measurements from the height of mature shrubs. We are interested in seeing whether the shrubs we observe in a particular region differ from those we have observed elsewhere, which we measured as having a median height of 1.65 m. We measure 100 plants and identify that 21 have a height less than 1.65 m
(a) What are the hypotheses I would use to test whether the typical height in the region of interest is different to the broader population?
(b) If H0 is true, what is the sampling distribution of the number of trees smaller than 1.65 m?
(c) Construct a 95% CI for the proportion smaller than the median.
(d) Determine the p-value for the same hypotheses, and use this to do a hypothesis test with α = 0.05.
Step by step
Solved in 3 steps with 2 images
