Let X1, …, Xn be a random sample from a N(μ, σ²) population. Find the MLEs of μ and of σ.

The height of corn stalks (in cm) have a N(μ1,σ1) distribution, while the height of Nebraska corn stalks have a N(μ2,σ2) distribution. It is known that σ1 ̸= σ2. A random sample of corn stalks from Iowa and Nebraska yielded the following summary statistics. Iowa: n1 =15 x ̄1 =155 s1 =16 Nebraska: n2 =17 x ̄2 =145 s2 =10 Suppose we wish to test H0 : μ1 = μ2 versus Ha : μ1 ̸= μ2 at the α = 0.10 significance level. What is the value of the test statistic (TS) and critical value (CV )? TS=2.09, CV=1.697 TS=2.09, CV=1.645 TS=2.15, CV=1.697 TS=2.15, CV=1.717 TS=2.15, CV=1.645 TS=2.09, CV=1.717

9. Let 7 = 1.135013 be the sample mean of an iid sample r1,..., T50 from a gamma population Gamma(1, 3). Here ß > 0 is the unknown paramcter of interest. Construct an approximate 95%-CI for ß.

R3