Question

It has been found that 85.5% of all enrolled college students in the united states are undergraduates. a random sample of 400 enrolled college students in a particular state revealed that 337 of them were undergraduates. state the null and alternate hypotheses to test whether the proportion differs from the national percentage. group of answer choices h0: p = 0.843h1: p = 0.855 h0: p ≠ 0.855h1: p = 0.855 h0: p = 0.855h1: p ≠ 0.855 h0: p = 0.855h1: p = 0.843

Answer 1

The correct pair of null and alternate hypotheses for testing whether the proportion of enrolled college students in a particular state differs from the national percentage is:

`\[ H_0: p = 0.855 \]`

`\[ H_1: p \\eq 0.855 \]`

Step-by-step explanation:

The null hypothesis
`(\(H_0\))` posits that the proportion of undergraduates in the particular state
`(\(p\))` is equal to the national percentage (0.855), while the alternate hypothesis
`(\(H_1\))` suggests that the proportion differs from the national percentage. This is a two-tailed test
`(\(\\eq\))` because we are interested in deviations in either direction from the national percentage.

In hypothesis testing, the null hypothesis represents the status quo or the assumption that there is no significant difference, while the alternate hypothesis challenges this assumption. The chosen hypotheses are appropriate for investigating whether the proportion of undergraduates in the state deviates from the national percentage.

To conduct the test, one would use a significance level (e.g., 0.05) and compare the p-value from the sample to determine whether there is enough evidence to reject the null hypothesis. The two-tailed nature of the test indicates interest in deviations in either direction, making it comprehensive for capturing any significant difference in the proportion of undergraduates in the state compared to the national percentage.

In conclusion, the hypothesis pair
`\(H_0: p = 0.855\)` and
`\(H_1: p \\eq 0.855\)`is the appropriate setup for investigating whether the proportion of undergraduates in the particular state significantly differs from the national percentage.