1

Below you are given a partial computer output based on a sample of 7 observations,relating an independent variable(x) and a dependent variable(y).

Predictor Coefficient Standard Error

Constant 24.112 8.376

X -0.252 0.253

Analysis of Variance

Source SS

Regression 196.893

Error 94.822

1.To test for the signifiance of the slope,what is the t test statistics?

A 3.222

B 2.650

C 3.986

D 4.126

2.To perform an F test, what is the F test statistic?

A 9.766

B 9.932

C 10.382

D 11.010

3.What is the coefficient of determination?

A 0.545

B 0.675

C 0.776

D 0.798

2)

The average amount of time boys and girls aged seven to 11 spend playing sports each day is believed to be the same. A study is done and data are collected, resulting in the data in the table below. Each populations has a normal distribution. Test the claim at a 0.05 level of significance. Sample Size (n) Mean Time (hrs) Sample Standard Deviation Population 1: Girls 9 2 0.866 Population 2: Boys 16 3.2 1.000 Ho: H1 H2 Ha: H1 # H2 t - Test Statistic = [Round to 2 decimals) p - Value = (Round to 4 decimals) Conclusion: There is sufficient evidence to (reject OR not reject) the claim Insert PriSoSuppose that we have n independent observations :1, ..., In from a normal distribution with mean / and variance o', and we want to test Ho : 0' = 1 H1:0->1 (a) Find the maximum likelihood estimator of / when the null hypothesis is true. (b) Calculate the Likelihood Ratio Test Statistic T = 2log (max L(u, 62) ) - 2 log max L(/, 1) (c) Explain as clearly as you can what happens to T when our estimate of o' is less than 1. (d) Show that the GLRT test is the same as a test which rejects the null hypothesis when s' > k