Question

it is believed that 11% of all americans are left - handed. a college needs to know how many left - handed desks to place in the big lecture halls being constructed on its campus. they have 16,343 students. in a random sample of 160 students, 25 were left - handed. does this provide enough evidence to show that students at this college have a higher percentage of left - handers than the general american population? use a 9% level of significance. i. identify hypothesis (a) what is the correct parameter symbol for this problem? p (a population proportion) (b) what is the wording of the parameter in the context of this problem? the proportion of students from this campus that are left - handed (c) fill in the correct null and alternative hypotheses: \\(h_0: p = 0.11\\) \\(h_a: p > 0.11\\) part 2 of 6 ii. choose the significance level, \\(\alpha\\) (d) the significance level (as a decimal) is: 0.09 (e) since categorical data was collected from each observational unit, what conditions do we need to check? check all that apply. \\(n \geq 10n\\), where \\(n\\) is the population size (hint: this one is required!) \\(np \geq 10\\) \\(n \geq 30\\) or normal population. \\(n(1 - \hat{p}) \geq 10\\) \\(n\hat{p} \geq 10\\) \\(\sigma\\) is known. \\(n(1 - p) \geq 10\\) \\(\sigma\\) is unknown.

Explanation:

Step1: Check N ≥ 10n

N = 16343, n = 160. 10n = 1600. 16343 ≥ 1600: true.

Step2: Check np ≥ 10

np = 160×0.11 = 17.6 ≥ 10: true.

Step3: Check n(1-p) ≥ 10

n(1-p) = 160×0.89 = 142.4 ≥10: true.

Step4: Ignore irrelevant conditions

Conditions like n≥30 (for means), σ known/unknown (for z/t tests), and sample proportion-based checks (n̂p, n̂(1-p)) don’t apply here.

Answer:

N ≥ 10n, where N is the population size (Hint: This one is required!), np ≥ 10, n(1-p) ≥ 10