Question

it is claimed that proportion in favor of proportion A is greater than 60%. A sample of size 100 found 69 in favor. what is the alternative hypothesis, and what is (are) the critical value

Answer 1

The alternative hypothesis is
`H_1: p > 0.6`.

The critical value is
`Z_c = 1.645`

Explanation:

It is claimed that proportion in favor of proportion A is greater than 60%.

This means that at the null hypothesis, we test if the proportion is of at most 60%, that is:

`H_0: p \leq 0.6`

At the alternative hypothesis, we test if the proportion is more than 60%, that is:

`H_1: p > 0.6`

What is (are) the critical value?

The critical value is the value of Z with a p-value 1 subtracted by the standard significance level of 0.05, since we are testing if the mean is more than a value, so, looking at the z-table,
`Z_c = 1.645`