nonparametic statistics the sign test, using the j table a) state hypothesis & c

Question

nonparametic statistics
the sign test, using the j table
a) state hypothesis & claim. b) find critical value. c) compute test value. d) make decision e) summarize results
a manufacturer believes that if routine maintenance ( cleaning and ikon of machines) is increased to occur a day rather than once a week, the number of defective parts produced by the machine will decrease. nine machines are selected & the number of defective parts produced over a 24 hour operating period is counted. maintenence is then increased to once a day for a week and the number of defective parts each machine produces is again counted over a 24 hour operating period. the data is below. at.   a=0.10. can the manufacturer conclude that increased maintenance reduces the number of defective parts manufacturers by the machines?
machine: 1 2 3 4 5 6 7 8 9
before:   6 18 5 4 16 13 20 9 3
after:   5 16 7 4 18 12 14 7 1

ho= h1=   cv=    tv=
decision =   question =

Explanation / Answer

a. H0:median difference is zero (there is no difference in number of defects before and after maintainence)

H1:median difference is greater than zero (there is improvement in terms of reduced defects after maintainence).

Critical value at n=9 (number of matched pairs), alpha=0.10, one-tailed test is: 3

Test value:

(Note: observations with zero difference is ignored)

z=sigma SRj/sqrt sigma SR^2j

=30/sqrt 201

=2.11

Decision: Reject H0, if smaller of the positive or negative signs is less than or equal to cv. Here, negative signs has the smaller number taht is 2, and it is less than 3. Therefore, reject H0, and conclude that mainetnance has reduced number of defects.

After Before D Sign Rank of D Signed rank 5 6 1 + 3.5 +3.5 16 18 2 + 6.0 +6 7 5 -2 - 1.5 -1.5 18 16 -2 - 1.5 -1.5 12 13 1 + 3.5 +3.5 14 20 6 + 8.0 +8.0 7 9 2 + 6.0 +6.0 1 3 2 + 6.0 +6.0 Sigma SRj=30

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