that are supposed to weigh exactly (on average) 10 ounces. A sample is taken: n=20 X = 10.20 oz s = 0.80 oz (a) Test at α = .05

You investigate the relationship between height and dbh (diameter at breast height) of oak trees. You get the following results: dbh (cm): 26 49 52 32 15 15 39 41 20 30 46 42 21 40 17 38 13 26 49 26height(m): 10.2 13.5 16.3 10.8 8.9 10.0 14.2 11.3 9.7 11.4 13.5 13.6 11.6 11.2 7.7 13.1 7.9 10.4 15.6 9.0 Read the data into R. (a) Calculate the following using R: ̄x , ̄y , SSx, SSy. (Note that to get SSy or SSx, you can just ask R for the variance (var) or standard deviation, and then do the appropriate calculation).(b) Perform a complete test of the hypothesis that there is no difference in height as dbh increases. Write out all the appropriate steps of a regular hypothesis test (give H0, H1, α, your decision, etc.)(c) Give the equation of the least squares line

For each of the following hypotheses (including test statistic and other information), find the p-value (or its bounds) and draw a basic conclusion with respect to (w.r.t.) Ho with 95% confidence. Assume normality in the populations or that the Central Limit Theorem otherwise applies.

A random sample from a normal population has:n = 8, X-bar = 16, and s = 3. Find the 95% PI for asingle new value from the population.