Question

Your statistics instructor claims that 55% of the students who take her Elementary Statistics class go through life feeling more enriched. For some reason that she can't quite figure out, most people don't believe her. You decide to check this out on your own. You randomly survey 60 of her past Elementary Statistics students and find that 34 feel more enriched as a result of her class. Do we detect that the actual percentage of students feeling enriched is different from 55%? Use ?=0.01.

Answer 1

Solution: Here, the given information are

n=60, x=34, p0=0.55, =0.01

= x/n = 34/60 = 0.5667

Null hypothesis: H0: p0=0.55

Alternative hypothesis: H1: p0 0.55

Test statistic:

Z=

=

z = 0.259

Using P-value approach

P-value=2*(1-P(z))

=2*(1-P(0.26))------------(0.259 round upto 0.26)

=2*(1-0.6026)

=2*0.3974

P-value = 0.7948

P-value is greater than the significance level 0.01.

From the P-value conclusion we Accept H0.

The actual percentage of students feeling enriched is not different from 55%.