Question

You wish to test the following claim (HaHa) at a significance level of α=0.02α=0.02.

      Ho:p1=p2Ho:p1=p2
      Ha:p1>p2Ha:p1>p2

You obtain 57.5% successes in a sample of size n1=228n1=228 from the first population. You obtain 45.7% successes in a sample of size n2=433n2=433 from the second population. For this test, you should NOT use the continuity correction, and you should use the normal distribution as an approximation for the binomial distribution.

What is the critical value for this test? (Report answer accurate to three decimal places.)
critical value =

What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =

Can you explain how to solve for the critical value using TI-84 calculator functions?

Answer 1

The critical value of the test is = = 2.054. (Ans).

The test-statistic is, Z = , where, = 0.575, = 0.457, = 228, = 433.

Hence, Z = 2.9094. (Ans).

In order to compute the test-statistic is calculator we have to first select normal distribution, then put 0 for mean and 1 for standard deviation. After that, we have to put 0.02 as cumulative probability.

Since, observed Z > critical value, we reject H0.