2. The following table shows a sample of students who use either Android phones

Question

2. The following table shows a sample of students who use either Android phones or iPhones. Results of a survey asking whether they use phones mainly for work or other purposes as follows:

A) What proportion of students mainly use their phones for work?

B) What proportion of Android users mainly use their phone for work? What proportion of iPhone users mainly use their phone for work? Which type of phone (Android/iPhone) is more likely to have work as their main use?

C) Assume that the proportion of all students who use their phones for work is 0.3, what is the sampling distribution of the proportion of students who use their phones for work if our sample size is 300 students?

D) How likely is it that would get a sample proportion less than what we obtained in part A?

Main use of phone/Phone type Android iPhone Total Work 40 70 110 Other 40 150 190 Total 80 220 300

Explanation / Answer

a)proportion of students mainly use their phones for work =110/300 =11/30 =0.3667

b)proportion of Android users mainly use their phone for work =40/80 =0.5

proportion of iPhone users mainly use their phone for work =70/220=7/22=0.3182

from above Android  users is more likely to have work as their main use

c)

here as p=0.3 and n=300 therefore np>=10 and n(1-p)>=10

hence sampling distribution of the proportion   follows normal distribution

with mean proportion =0.3

and

c)

probability to  get a sample proportion less than 0.3667

std error of proportion=?p=?(p*(1-p)/n)= 0.0265

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