A survey claims that 8 out of 10 doctors recommend a specifi

A survey claims that 8 out of 10 doctors recommend a specific treatment for their patients with the flu. To test this claim against the alternative that the actual proportion of doctors who recommend this treatment is less than 0.80, a random sample of 250 doctors results in 183 who indicate that they recommend this specific treatment. The value of the test statistic in this problem is approximately equal to

Solution

given n= 250

p = 183/250 = 0.732

test static Z = sqrt( p * (1-p) /n)

substitute the above values we get Z = 0.028