Question

The article "Facebook Use and Academic Performance Among College Students"† estimated that 87% percent of students at a large public university in California who are Facebook users update their status at least two times a day. Suppose that you plan to select a random sample of 600 students at your college. You will ask each student in the sample if they are a Facebook user and if they update their status at least two times a day. You plan to use the resulting data to decide if there is evidence that the proportion for your college is different from the proportion reported in the article for the college in California. What hypotheses should you test?

H₀: p = 0.87 versus H_a: p > 0.13

H₀: p = 0.87 versus H_a: p ≠ 0.87  

  H₀: p = 0.87 versus H_a: p > 0.87

H₀: p = 0.13 versus H_a: p ≠ 0.87

H₀: p = 0.87 versus H_a: p < 0.87

Answer 1

According to the question

87% percent of students at a large public university in California who are Facebook users update their status at least two times a day.

and we are asked  if there is evidence that the proportion for college is different from the proportion reported in the article for the college in California

it is a two tailed test

so null and alternative hypothesis will be

H₀: p = 0.87 i.e there is no significant difference the the proportion of facebook users in the college and claimed proportion.

versus H_a: p ≠ 0.87 i.e proportion for college is different from the proportion reported in the article for the college in California

option 2 is correct