(In some of the exercises that follow, we must
Chapter 8, Problem 7E(choose chapter or problem)
Let \(X\) and \(Y\) equal the number of milligrams of tar in filtered and non-filtered cigarettes, respectively. Assume that the distributions of \(X\) and \(Y\) are \(N\left(\mu_{X}, \sigma_{X}^{2}\right)\) and \(N\left(\mu_{\gamma}, \sigma_{y}^{2}\right)\), respectively. We shall test the null hypothesis \(H_{0}: \mu_{X}-\mu_{Y}=0\) against the alternative hypothesis \(H_{1}: \mu_{X}-\mu_{y}<0\), using random samples of sizes \(n=9\) and \(m=11\) observations of \(X\) and \(Y\), respectively.
(a) Define the test statistic and a critical region that has an \(\alpha=0.01\) significance level. Sketch a figure illustrating this critical region.
(b) Given \(n=9\) observations of \(X\), namely,
0.9 1.1 0.1 0.7 0.4 0.9 0.8 1.0 0.4
and m = 11 observations of Y, namely,
1.5 0.9 1.6 0.5 1.4 1.9 1.0 1.2 1.3 1.6 2.1
calculate the value of the test statistic and state your conclusion clearly. Locate the value of the test statistic on your figure.
Equation Transcription:
Text Transcription:
X
Y
N(mu_X, sigma_X^2)
N(mu_Y, sigma_Y^2)
H_0:mu_X-mu_Y=0
H_1:mu_X-mu_y<0
n=9
m=11
alpha=0.01
Unfortunately, we don't have that question answered yet. But you can get it answered in just 5 hours by Logging in or Becoming a subscriber.
Becoming a subscriber
Or look for another answer