Question

a student at corona del sol is making the claim that the probability a randomly selected 17 year old at corona has a part time job is 0.68. you believe the proportion is actually higher.

a. identify the null and alternative hypotheses.
$h_0:$ select an answer ?
$h_a:$ select an answer ?

b. explain what it would mean to make a type i or type ii error in the context of the problem. what possible issues could result from making this type of error?
type i error

type ii error

Explanation:

For part a: The null hypothesis states the claimed proportion, and the alternative hypothesis reflects the belief that the proportion is higher. For part b: A Type I error is rejecting a true null hypothesis, while a Type II error is failing to reject a false null hypothesis, both framed in the context of the part-time job proportion claim.

Answer:

a.
$H_0$: $p = 0.68$
$H_A$: $p > 0.68$

b.
Type I error: Concluding that the proportion of 17-year-olds at Corona del Sol with a part-time job is higher than 0.68, when in reality the proportion is equal to 0.68. This could lead to incorrect resource allocation (e.g., planning more part-time job support programs that aren't actually needed) or misleading claims about student employment rates.
Type II error: Failing to conclude that the proportion of 17-year-olds at Corona del Sol with a part-time job is higher than 0.68, when in reality the proportion is higher than 0.68. This could mean missing the opportunity to address actual higher student employment needs (e.g., not providing necessary scheduling support for working students) or ignoring a true shift in student employment patterns.