Question

Suppose a random sample of 100 observations from a binomial population gives a value of \(\hat p = .63\) and you wish to test the null hypothesis that the population parameter p is equal to .70 against the alternative hypothesis that p is less than .70.

a. Noting that\(\hat p = .63\) what does your intuition tell you? Does the value of \(\hat p\) appear to contradict the null hypothesis?

Short answer

1. The population parameter may be less than .70 as the sample proportion comes out to be less than 0.70.

Step-by-step solution

Given Information

The hypothesis are given by

\(\begin{aligned}{H_0}:p = .70\\{H_a}:p < .70\end{aligned}\)

The sample size is 100

Sample size

A group selected from a population is a sample. Samples are taken from the population. Sample size tell us how many people from the population are included in the sample.

Step 3:

The difference is .70. The sample mean is .63. The intuition tells us that the value of .70 is not necessarily wrong; it is possible that the true mean is actually below 0.70.