In a recent survey, 55% of employed adults reported that basic mathematical skil

Question

In a recent survey, 55% of employed adults reported that basic mathematical skills were critical or very important to their job. The supervisor of the job placement office at a 4-year college thinks this percentage has increased due to increased use of technology in the workplace. She takes a random sample of 450 employed adults and finds that 266 of them feel that basic mathematical skills are critical or very important to their job. Is there sufficient evidence to conclude that the percentage of employed adults who feel basic mathematical skills are critical or very important to their job has increased at the alpha = 0.01 level of significance? What are the null and alternative hypotheses? A. H_0: p = 0.55 versus H_1: p > 0.55 B. H_0: p = 0.55 versus H_1: p notequalto 0.55 C. H_0: p = 0.55 versus H_1: p

Explanation / Answer

(a) Option A

(b)

Data:    

n = 450   

p = 0.55   

p' = 0.5911111   

Hypotheses:   

Ho: p 0.55   

Ha: p > 0.55   

Decision Rule:   

= 0.01   

Critical z- score = 2.326347874

Reject Ho if z > 2.326347874

Test Statistic:   

SE = {(p (1 - p)/n} = (0.55 * (1 - 0.55)/450) = 0.023452079

z = (p' - p)/SE = (0.591111111111111 - 0.55)/0.0234520787991171 = 1.75

(c) p- value = 0.040

(d) Option B

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