In a recent survey, 43% of employed U.S. adults reported that basic mathematical

Question

In a recent survey, 43% of employed U.S. 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 800 employed adults and finds that 354 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 =0.1 level of significance?

Can I solve this on a ti-84?

Explanation / Answer

we are given that P = 0.43

and sample proportion as = 354/800 = 0.4425

now the standard deviation is given as

= sqrt[ P * ( 1 - P ) / n ] = sqrt(0.43*(1-0.43)/800) = 0.017

The test statistic is a z-score (z) defined by the following equation.

z = (p - P) /

Z = (0.4425-0.43)/0.017 = 0.735

now we calculate the z value for alpha = 0.1

is - 1.28

now as our z stat > z critical hence we can reject the null hypothesis and conclude that  the percentage of employed adults who feel basic mathematical skills are critical or very important to their job has increased

H0 :  the percentage of employed adults who feel basic mathematical skills are critical or very important to their job has not increased

H1: the percentage of employed adults who feel basic mathematical skills are critical or very important to their job has increased

Hope this helps !!

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