Question

question 9
a company president believes that 60% of the shareholders of the company read the annual report. the local business magazine says the number of actual shareholders is quite below 60%.
what are the hypotheses for this test?

• $h_0: p = 0.60$ $h_a: p < 0.60$
• $h_0: p = 0$ $h_a: p \

eq 0$

• $h_0: p \leq 0.55$ $h_a: p > 0.55$
• $h_0: p \geq 0.55$ $h_a: p < 0.55$

Explanation:

The null hypothesis ($H_0$) is the claim we test, here the company president's belief that 60% (so \( p = 0.60 \)) of shareholders read the annual report. The alternative hypothesis ($H_a$) is the local business magazine's claim that the actual proportion is below 60% (so \( p < 0.60 \)). We check the options: the first option has \( H_0: p = 0.60 \) and \( H_a: p < 0.60 \), which matches. Other options have incorrect \( p \)-values or directions.

Answer:

A. \( \text{H}_0: p = 0.60 \quad \text{H}_a: p < 0.60 \)