Answer: 385
Step-by-step explanation:
Given : In a sample of 60 stores of a certain company, 50 violated a scanner accuracy standard.
Let p be the true proportion of the stores that violate the standard.
Since , it has been demonstrated that the conditions for a valid large-sample confidence interval for p were not met.
So , to get accurate result , we take [tex]p=0.5[/tex] (It will give the minimum required sample size when prior information about p is not given )
Formula to find sample size : [tex]n=p(1-p)(\frac{z}{E})^2[/tex], where z= critical z-value for confidence interval and E is the margin of error
Since , E=0.05 and Critical z-value for 95% confidence=1.96
[tex]\Righatrrow\ n= (0.5)(0.5)(\frac{1.96}{0.05})^2=384.16\approx385[/tex]
Hence, the number of stores that must be sampled= 385.
