The business college computing center wants to determine the proportion of business students who have laptop computers. If the proportion exceeds $25 \%$, then the lab will scale back a proposed enlargement of its facilities. Suppose 250 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 $\mathrm { n }$ satisfies $n \geq 30$.
C) The sample proportion is close to 5 .
D) The population has an approximately normal distribution.

Question

Quizplus · Accepted Answer

The assumptions necessary for this test include that the sample size $n$ satisfies both $n p_0 \geq 15$ and $n q_0 \geq 15$, where $p_0$ is the hypothesized proportion (in this case, 25% or 0.25) and $q_0 = 1 - p_0$. This condition ensures that the sampling distribution of the sample proportion can be approximated by a normal distribution, which is crucial for conducting the hypothesis test properly.

The Business College Computing Center Wants to Determine the Proportion 25%25 \%25%

The Business College Computing Center Wants to Determine the Proportion $25 \%$