(In some of the exercises that follow, we must

Chapter 9, Problem 8E

(choose chapter or problem)

Different sizes of nails are packaged in "1-pound" boxes. Let \(X_{i}\) equal the weight of a box with nail size (4i) \(C, i=1,2,3,4,5\), where \(4 C, 8 C, 12 C, 16 C\), and \(20 C\) are the sizes of the sinkers from smallest to largest. Assume that the distribution of \(X_{i}\) is \(N\left(\mu_{i}, \sigma^{2}\right)\). To test the null hypothesis that the mean weights of "1-pound" boxes are all equal for different sizes of nails, we shall use random samples of size 7, weighing the nails to the nearest hundredth of a pound.

(a) Give a critical region for an \(\alpha=0.05\) significance level.

(b) Construct an ANOVA table and state your conclusion, using the following data:

(c) For each set of data, construct box-and-whisker diagrams on the same figure and give an interpretation of your diagrams.

Equation Transcription:

 

 

Text Transcription:

X_i  

C,i=1,2,3,4,5

4C,8C,12C,16C

20C X_i  

N(mu_i,sigma^2)

alpha=0.05