7. A random sample of 55 cell phones used by students revealed that 5 of them ha

Question

7. A random sample of 55 cell phones used by students revealed that 5 of them had malware. (6 pts) (a) Find a 95% two-sided confidence interval on the true proportion of cell phones with (b) Using the point estimate of p from the 55 phones, how many phones must be tested to be (c) How large must the sample be if we wish to be at least 90% confident that the error in malware. 90% confident that the tolerance in estimating p was less than 0.05? estimating p is less than 0.05 regardless of the true value of p?

Explanation / Answer

a)

b)

c)

for no estimate p=0.5

                                                                                           x                    =   5 sample size n                    = 55 sample proportion     p x/n= 0.0909 std error       =Se            =(p*(1-p)/n) = 0.0388 for 95 % CI value of z= 1.9600 margin of error E=z*std error                            = 0.0760 lower confidence bound=sample proportion-margin of error 0.015 Upper confidence bound=sample proportion+margin of error 0.167

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