Question

A survey claims that 9 out of 10 doctors (i.e., 90%) recommend Kiva for their patients who have children. To test this claim at a = 0.05, against the alternative that the actual proportion of doctors who recommend Kiva is less than 90%, a random sample of 100 doctors results in 83 who indicate that they recommend Kiva. Based on the data is it the case that 90% of doctors recommend drugs to parents so they can deal with their children?

A) State the hypothesis:

B) Critical value

C) Test statistic and decision about Ho

D) The conclusion about the problem statement.

Answer 1

a)

H0: p = 0.90

Ha: p < 0.90

b)

Critical value = -1.645 (From Z table)

c)

Sample proportion = 83 / 100 = 0.83

Test statistics = ( - p ) / sqrt [ p ( 1 - p) / n ]

= ( 0.83 - 0.90) / sqrt [ 0.90 ( 1 - 0.90) / 100 ]

= -2.33

Decision - Since test statistics < -1.645 , Reject H0.

d)

Conclusion = We have sufficient evidence to support the claim that the actual proportion of doctors who

recommend Kiva is less than 90%.