# hypothesis test for proportion

In this case we must start by an “a priori” assumption about the value of the proportion of the population, p. Then we use , the sample proportion, which is calculated by obtaining a random sample from the population to determine if this assumption about p is likely. So we will follow these steps:

Example: It is believed that in the Autonomous Community of Castilla and Leon the same number of males and women taking midlevel studies is the same. We took a random sample of 1000 school records and found that 532 corresponded to males and 468 were females. Is this outcome unlikely or does it fit the vast majority of 99 % of the results ?

Step 1: H0: p ≤ 0.5; H1: p > 0.5.

Step 2: This is a one-tailed test with α = 0.01, then the critical value zα = 2.33 and I = (-∞,0.5368)

Step 3:

Step 4: z < zα, we accept the null hypothesis, so we can’t reject the belief that both men and women do these studies in the same number

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