The business college computing center wants to determine the proportion of business students who have laptop computers. If the proportion exceeds 35%, then the lab will scale back a proposed enlargement of its facilities. Suppose 300 business students were randomly sampled and 75 have laptops. What assumptions are necessary for this test to be satisfied?

A) The sample size $n$ satisfies both $n p _ { 0 } \geq 15$ and $n q _ { 0 } \geq 15$.
B) The sample size $n$ satisfies $n \geq 30$.
C) The population has an approximately normal distribution.
D) The sample proportion is close to $.5$.

Question

The business college computing center wants to determine the proportion of business students who have laptop computers. If the proportion exceeds 35%, then the lab will scale back a proposed enlargement of its facilities. Suppose 300 business students were randomly sampled and 75 have laptops. What assumptions are necessary for this test to be satisfied?

A) The sample size $n$ satisfies both $n p _ { 0 } \geq 15$ and $n q _ { 0 } \geq 15$.
B) The sample size $n$ satisfies $n \geq 30$.
C) The population has an approximately normal distribution.
D) The sample proportion is close to $.5$.

Quizplus · Accepted Answer

The assumptions necessary for this test are that the sample size $n$ satisfies both $n p _ { 0 } \geq 15$ and $n q _ { 0 } \geq 15$, where $p_0$ is the hypothesized population proportion and $q_0 = 1 - p_0$. This ensures the sampling distribution of the sample proportion is approximately normal.

The Business College Computing Center Wants to Determine the Proportion nnn

The Business College Computing Center Wants to Determine the Proportion $n$