Question
Less than 23% of workers indicate that they are dissatisfied with their job. Express the null and alternative hypotheses in symbolic form for this claim (enter as a percentage).
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GPT-4o mini
To express the null and alternative hypotheses in symbolic form for the claim that less than 23% of workers are dissatisfied with their job, we can define the population proportion of workers who are dissatisfied as \( p \).
**Null Hypothesis (\( H_0 \)):** This states that the proportion of workers who are dissatisfied is equal to or greater than 23%.
\[
H_0: p \geq 0.23
\]
**Alternative Hypothesis (\( H_a \)):** This states that the proportion of workers who are dissatisfied is less than 23%.
\[
H_a: p < 0.23
\]
Thus, the symbolic expressions for the hypotheses are:
- \( H_0: p \geq 0.23 \)
- \( H_a: p < 0.23 \)
**Null Hypothesis (\( H_0 \)):** This states that the proportion of workers who are dissatisfied is equal to or greater than 23%.
\[
H_0: p \geq 0.23
\]
**Alternative Hypothesis (\( H_a \)):** This states that the proportion of workers who are dissatisfied is less than 23%.
\[
H_a: p < 0.23
\]
Thus, the symbolic expressions for the hypotheses are:
- \( H_0: p \geq 0.23 \)
- \( H_a: p < 0.23 \)
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