Question

A two-tailed test was conducted with the null and alternative hypotheses stated being \({H_0}:p = .69\) against \({H_a}:p \ne .69\), respectively, with a sample size of 150. The test results were z = -.98 and two-tailed p-value = .327

a. Determine the conditions required for a valid large sample test

Short answer

1. The sample is drawn from a binomial population. The sample size is large. These conditions are required for a valid large sample test.

Step-by-step solution

Given Information

The hypothesis are given by

\(\begin{aligned}{H_0}:p = .69\\{H_a}:p \ne .69\end{aligned}\)

The z-statistic is -.98..

The p-value is .327

Calculate np and nq

For \(n = 150\,and\,p = .69\)

\(\begin{aligned}np &= 150 \times 0.69\\ &= 103.5\\nq &= 150 \times 0.31\\ &= 46.5\end{aligned}\)

Here, np and nq both are greater than 15.

Step 3:

The sample is drawn from a binomial population. The sample size is large. These conditions are required for a valid large sample test.