The average cost of tuition, room and board at small private liberal arts colleges is reported to be $8,500 per term, but a financial administrator believes that the average cost is higher. A study conducted using 350 small liberal arts colleges showed that the average cost per term is $8,745 with a standard deviation of $1,200. Let = 0.05. What are the null and alternative hypotheses for this study? A) Null: µ $\le$$9,000; alternative: µ $9,000 B) Null: µ $\ge$ $9,000; alternative: µ $8,500 D) Null: µ $\ge$ $8,500; alternative: µ

Question

The average cost of tuition, room and board at small private liberal arts colleges is reported to be $8,500 per term, but a financial administrator believes that the average cost is higher. A study conducted using 350 small liberal arts colleges showed that the average cost per term is $8,745 with a standard deviation of $1,200. Let = 0.05. What are the null and alternative hypotheses for this study? A) Null: µ $\le$$9,000; alternative: µ > $9,000 B) Null: µ $\ge$ $9,000; alternative: µ < $9,000 C) Null: µ $\le$ $8,500; alternative: µ > $8,500 D) Null: µ $\ge$ $8,500; alternative: µ < $8,500

Quizplus · Accepted Answer

The null hypothesis should always state that there is no significant difference or effect, so in this case, the null hypothesis should state that the average cost per term is equal to or less than $8,500 (which is the reported average cost). The alternative hypothesis should state that the average cost per term is higher than $8,500, since the financial administrator believes that it is higher. Therefore, Choice C correctly states the null hypothesis as µ ≤ $8,500 and the alternative hypothesis as µ > $8,500.

The Average Cost of Tuition, Room and Board at Small ≤\le≤

The Average Cost of Tuition, Room and Board at Small $\le$