Question

In a survey of 500 students aged 12-18, it is found that 82% use computers in school. Test the claim that the proportion of students aged 12-18 who use computers in school is equal to ¾.  α = 0.03

Answer 1

Sol:

Ho:p=3/4=0.75

Ha : p not =0.75

alpha=0.03

calculation of test statistic

z=p^-p/sqrt(p*(1-p)/n)

p^=0.82

n=500

p=0.75

z=(0.82-0.75)/sqrt(0.75*(1-0.75)/500)

z=3.614784

calculation of p value

p value in excel

2*left tail prob

left tailprob in excel is

==NORM.S.DIST(-3.614784,TRUE)

=0.000150299
0.000300598

2*let tail=2*0.000150299=0.000300598

statistical decision:

p value=0.0003

p<0.03

Reject Ho

Accept Ha

conclusion:

There is no suffcient statistical evidence at 3% level of significance to support the claim that  the proportion of students aged 12-18 who use computers in school is equal to ¾.