A sample of mothers was asked how old they were when their first child was born. The following display from a TI-84 Plus calculator presents the results of a hypothesis test regarding the proportion who had their first child before the age of 24.

Question

1-PropZTest
prop does not = .3
z= 2.605087778
p=.0091850726
^p=.4516129032
n=65

what are the null and alternate hypothesis

Answer 1

In this context, where you are testing the proportion of mothers who had their first child before the age of 24, the hypotheses can be formulated as follows:

• Null Hypothesis (\(H_0\)): The proportion of mothers who had their first child before the age of 24 is equal to 0.3. Mathematically, this can be stated as: \[ H_0: p = 0.3 \]

• Alternative Hypothesis (\(H_a\)): The proportion of mothers who had their first child before the age of 24 is not equal to 0.3. This is a two-tailed test and can be stated as: \[ H_a: p \neq 0.3 \]

Here, \(p\) represents the true proportion of mothers who had their first child before the age of 24. The test checks for any significant difference from the hypothesized proportion of 0.3.