Question

For the binomial sample sizes and null hypothesized values of p in each part, determine whether the sample size is large enough to use the normal approximation methodology presented in this section to conduct a test of the null hypothesis \({H_0}:p = {p_0}\)

1. \(n = 900,\;{p_0} = .975\)

Short answer

1. The sample size is enough to use the normal approximation.

Step-by-step solution

Given Information

Let p represents the probability.

We want to be sure that sample size is large enough to ensure that the normal approximation of\(\hat p\)is reasonable.

We check to see if \(n{p_0} \ge 15\;and\,n{q_0} \ge 15\)

Null hypothesis

A null hypothesis is a statistical supposition that claims there is no difference between specific features of a population as well as data-generating activity. The alternate hypothesis asserts that there is a distinction. Hypothesis test enables you to reject a null hypothesis with a particular confidence level.

Step 3:

Given that,

\(\begin{aligned}n &= 900,\;{p_0} &= 0.975\\then\,{q_0} &= 1 - {p_0} &= 0.025\\n{p_0} &= 877.5\\n{q_0} &= 22.5\end{aligned}\)

Here we observed that \(n{p_0}\) is greater than 15, therefore the sample size is enough to use the normal approximation.