Question

Problem: A large, public university wants to determine if a majority of its students use iPhones. The university randomly selects 122 of its students and asks each student whether or not they use an iPhone. Eighty (80) of these 122 students use an iPhone.

Question: Do the data provide evidence that more than 50% of all students at the university carry an iPhone? Use α = 0.05.

Answer 1

we have to test that if a majority of students use iPhones

so let P is proportion of students who use iPhones so

H0: P=0.5           Ha:P>0.5

we have

sample size=n=122

no.of students who uses iphone=x=80

so sample proportion is given by

now test statistics is given by

Test is right tailed so

P-value =P(Z>3.53) =0.0002

since P value is less than level of significance hence we reject H0 that means there are enough evidence to conclude that proportion is more than 0.5