Question

Samsung needs to estimate the battery function for the Galaxy Note 7. They take a random sample of 100 smartphones and discover that 10 of them contain defective batteries. Build a 90% confidence interval for the true proportion of defective batteries.

Answer 1

Sample size= n=100

And , number of phones containing defective batteries= x= 10

So, required proportion of defective batteries=p(cap)= x/n= 10/100= 0.10

Now, q (cap)= 1-p(cap)= 1-0.10= 0.90

Now, standard error of p(cap)= √(p*q/n)= √(0.10*0.90/100)= 0.03

Critical value = z( alpha= 10%=0.10)= 1.645

Therefore, 90% confidence interval for population proportion of defective batteries is given by

p( cap) ± z(alpha= 0.10)* std. error (p cap)

= 0.1± 1.645*0.03

=0.1±0.04935= 0.05065, 0.14935 ≈( 0.05,0.15)

So, 0.05 < P < 0.15