TEST OF HYPOTHESIS ABOUT A POPULATION PROPORTION, p

The strength of a pesticide may be measured by the proportion of pests that it kills. One pesticide advertises that if used properly it kills at least 99% of the pests. To see if the advertised figure is correct, 1000 pests are selected at random, exposed to the pesticide following the directions carefully, and 980 of them are killed. At a .10 level of significance, is there sufficient evidence to conclude that the advertised figure of 99% is too high?

 

SOLUTION

The parameter of interest is p, the proportion of pests the pesticide actually kills.

         H0: p = .99        Ha: p < .99

         Decision Rule: Accept Ha if the calculated p-value < .10.

        

         Calculations: n = 1000, p = 980/1000 = .98

                              

                                p-value = p(z < -3.18) = .5 - .4993 = .0007

Interpretation: At the .10 level of significance I conclude that the percentage of pests killed by this pesticide is less than 99%.

 

 

 

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