A researcher wanted to investigate whether life satisfaction differed between high school students, college students, and college graduates in the workplace. Thirty people from each of the groups were selected and their life satisfaction was determined. Which of the following tests should he run on the data? One-way between ANOVA Repeated measures ANOVA Correlation Chi-square

A hospital was interested in purchasing new thermometers for its Emergency Department. There were two different thermometer devices that were identified as being potentially suitable for purchase. The procurement officer asked nine Emergency Department nurses to use both thermometer devices during a shift. At the end of the shift, the officer asked them to rate how useable both devices were on a scale from 1 (not at all useable) to 7 (extremely useable). The data was non-normal. Assuming there were two zero-valued difference scores excluded from the analysis, and with an alpha level of .05, what is the critical value for the test?     2.306     2     4     3

Aspirin prevents blood from clotting and helps prevent strokes. The Second European Stroke Prevention Study asked whether adding another anticlotting drug named dipyridamole would make a difference for patients who had already had a stroke. Here are the data on strokes during the two years of the study: Aspirin alone Apsirin & Dipyridamole Number of Patients This test is two-tailed. What is the test statistic? 200 200 # Is there a significant difference in the proportion of strokes in the two groups? Test at a = 0.10. Round your answers to three decimal places, and round any interim calculations to four decimal places. Fill in the hypotheses below where p₁ denotes the proportion of patients in the aspirin group who suffered a stroke and på denotes the proportion of patients in the aspirin & dipyridamole group who suffered a stroke. Ho: P Ha: P₁ Number of Strokes P₂ 60 P₂ 54 Part 2 of

= Q1. Suppose that for k = 1,..., K and i 1,...,nk we observe independent Xki ~ Np(µk, Ip), where K, n₁,...,nk € N. In this question we consider the K-sample testing problem, where we want to test the null hypothesis Ho: μ₁ = μK. Note that the observations here have identity covariance matrix, so this is a simplification of the setting found in the notes. (a) Write down the likelihood function L(µ₁,…,‚µK) for this model, and prove that -X₁²), supμERP L(μ,..., μl) L(µ₁, ´μ1,...,KERP sup =... (ii) Show that we may write .., MK) = = K ink K where X₁ = n²¹ [₁ Xki and X = N-¹Σk_₁ nķīk with N = Σk 1_1 nk. -k i=1 k=1 exp 2 k=1 (b) In this part of the question we will find the distribution of K_₁7k|Xk – X² under Hō. (i) Define the Kp-dimensional random vector Y = (√n₁×¹, ..√nKX). Give, with jus- nk tification, the distribution of Y. K Σ k=1 (c) Suppose that we have data on K observe = nk Xk (√n₁(×₁ – Ī)¹,..., √nk(Xk — X)¹)¹ = (Ikp — N−¹VV¹)Y, where V is the Kp × p matrix given by VT =…