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Need help with filling the blanks on this one

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Need help with filling the blanks on this one. Part of it has already been answered. I need help filling in where there are "??" question marks. 

CMV infection and coronary restenosis. Exercise 18.3 found that 43% of CMV+ experienced arterial restenosis within 6 months of atherectomy. In contrast, 8% of CMV- patients experienced a similar outcome. Table 18.8 contains observed counts.

 

  1. Repeat the test with a z-statistic. Show the relation between the chi-square statistic and the z-statistic.

[Even though the book asks for the z test, the sample size requirements are not met for the z test.  Just proceed anyway, noting the issue]

Hypotheses:

H0: ??

Ha: ??

 

Assumptions

?????

 

We use Stata to compute our test statistic and P-value:
. prtesti 49 0.42857 26 0.07692, level(95)

 

Two-sample test of proportions                     x: Number of obs =       49

                                                   y: Number of obs =       26

------------------------------------------------------------------------------

             |       Mean   Std. Err.      z    P>|z|     [95% Conf. Interval]

-------------+----------------------------------------------------------------

           x |     .42857   .0706959                      .2900085    .5671315

           y |     .07692    .052258                     -.0255038    .1793438

-------------+----------------------------------------------------------------

        diff |     .35165   .0879137                      .1793424    .5239576

             |  under Ho:   .1118792     3.14   0.002

------------------------------------------------------------------------------

        diff = prop(x) - prop(y)                                  z =   3.1431

    Ho: diff = 0

 

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0

Pr(Z < z) = 0.9992         Pr(|Z| > |z|) = 0.0017          Pr(Z > z) = 0.0008

 

Results:   ???

 

Interpretation: ??????

Conclusion:  ????


Relationship between z stat and chisquare stat: ????

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