Solution Found!
Analyzing contrasts. Answer the following questions for
Chapter , Problem 12.42(choose chapter or problem)
Analyzing contrasts. Answer the following questions for the two contrasts that you defined in Exercise 12.41.
(a) For each contrast give \(H_{0}\) and an appropriate \(H_{a}\). In choosing the alternatives you should use information given in the description of the problem, but you may not consider any impressions obtained by inspection of the sample means.
(b) Find the values of the corresponding sample contrasts \(c_{1}\) and \(c_{2}\).
(c) Calculate the standard errors \(\mathrm{SE}_{c_{1}}\) and \(\mathrm{SE}_{c_{2}}\).
(d) Give the test statistics and approximate P-values for the two significance tests. What do you conclude?
(e) Compute 95% confidence intervals for the two contrasts.
Questions & Answers
QUESTION:
Analyzing contrasts. Answer the following questions for the two contrasts that you defined in Exercise 12.41.
(a) For each contrast give \(H_{0}\) and an appropriate \(H_{a}\). In choosing the alternatives you should use information given in the description of the problem, but you may not consider any impressions obtained by inspection of the sample means.
(b) Find the values of the corresponding sample contrasts \(c_{1}\) and \(c_{2}\).
(c) Calculate the standard errors \(\mathrm{SE}_{c_{1}}\) and \(\mathrm{SE}_{c_{2}}\).
(d) Give the test statistics and approximate P-values for the two significance tests. What do you conclude?
(e) Compute 95% confidence intervals for the two contrasts.
ANSWER:Step 1 of 6
Referring to the answers from the previous exercise, the null and alternative hypothesis for the first contrast are
\(\begin{array}{l} \mathrm{H}_{01}: \psi=0 \\ \mathrm{H}_{a 1}: \psi \neq 0 \end{array}\)
and the null and alternative hypothesis for the second contrast are
\(\begin{array}{l} \mathrm{H}_{02}: \psi=0 \\ \mathrm{H}_{a 2}: \psi \neq 0 \end{array}\)