In: Statistics and Probability
1. The numbers below represent heights (in feet) of 3-year old
elm trees. 5.1, 5.5, 5.8, 6.1, 6.2, 6.4, 6.7, 6.8, 6.9, 7.0, 7.2,
7.3, 7.3, 7.4, 7.5, 7.7, 7.9, 8.1, 8.1, 8.2, 8.3, 8.5, 8.6, 8.6,
8.7, 8.7, 8.9, 8.9, 9.0, 9.1, 9.3, 9.4, 9.6, 9.8, 10.0, 10.2,
10.2
Using the chi-square goodness-of-fit test, determine whether the
heights of 3-year old elm trees are normally distributed, at
the
a =.05 significance level. Also, find the p
value.
Suppose that X is normal, where µ is known and σ2 is unknown, and
let X1, …, Xn be a random sample from X. Let ?2 ̂ = 1 ? ∑ (?? − ?)2
? ?=1 .