To formulate the null and alternative hypotheses for the conjecture regarding the proportion of homes with extinguishers being 0.80, we can define them as follows:
a) Null Hypothesis (H0): This is the statement we assume to be true unless we have strong evidence to suggest otherwise. In your case, it states that the population proportion of homes with extinguishers is equal to 0.80.
b) Alternative Hypothesis (H1 or Ha): This is the statement we accept if the null hypothesis is rejected. It reflects a statement of a difference or effect that we might be interested in. In this case, it implies that the proportion of homes with extinguishers is not equal to 0.80.
So, we can summarize the hypotheses as:
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Null Hypothesis (H0): \( p = 0.80 \)
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Alternative Hypothesis (H1): \( p \neq 0.80 \)
This is a two-tailed test, as the alternative hypothesis is testing for any difference, whether it is greater than or less than 0.80.