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A drug company claims that fewer than 1% of pills that it produces and ships fail to retain full potency after 60 days of production. An inspector inspects a shipment of medications to determine the efficacy in terms of the proportion p in the shipment that failed to retain full potency after 60 days of production. To do so, she selects an SRS of 200 pills. Suppose that eight of the 200 pills have failed to retain their full potency. The test statistic for the proportion of pills that have failed to retain their potency is:

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JeanaShupp

Answer: 4.264

Step-by-step explanation:

Let  p be the proportion of pills that it produces and ships fail to retain full potency after 60 days of production.

Given claim : A drug company claims that fewer than 1% of pills that it produces and ships fail to retain full potency after 60 days of production.

i.e. [tex]p<0.01[/tex]

Sample size : [tex]n=200[/tex]

The proportion of pills in the sample that it produces and ships fail to retain full potency after 60 days of production : [tex]\hat{p}=\dfrac{8}{200}=0.04[/tex]

The test statistic for proportion is given by :-

[tex]z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}\\\\\\\Rightarrow\ z=\dfrac{0.04-0.01}{\sqrt{\dfrac{0.01(0.99)}{200}}}\\\\\\\Rightarrow\ z=4.2640143271\approx4.264[/tex]

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