Question

The pap smear test rate is estimated to be 0.50 with standard error 0.01 for the Acme HMO and is estimated to be 0.45 with standard error 0.01 for the Xanadu PPO. Is the difference statistically significant at significance level 5 percent? Explain your answer

Answer 1

Null hypothesis : There is no difference between the smear test rate of Acme HMO and Xanado PPO.

Alternative hypothesis : There is difference between the smear test rate of Acme HMO and Xanado PPO.

Test statistic is given by -

​​​​​​

where,

is the sample test rate of Acme HMO = 0.50 is the sample test rate of Xanado PPO = 0.45 is the standard Error of test rate of Acme HMO = 0.01

is the standard Error of test rate of Xanado PPO = 0.01

So, the value of the test statistic will be -

  

= 3.57

This can be tested from the critical value of t with given degree of freedom at 0.05 level of significance.

If value of the test statistic > critical value of t, null hypothesis may be rejected otherwise accepted.