Question

Social Media Addiction. Researchers are concerned about the impact of Social Media (Face- book, Twitter, Instagram, etc.) on student's focus. In particular, they believe that too much time spent on social media can negatively impact a student's academic performance. The lem has gotten worse with the recent widespread use of smartphones. The first o researchers is to find out, on average, how many hours per day on weekdays college students in the US spend on social media while using their smartphone. A random sample of 256 students resulted in a sample mean of 3.1 hours spent per weekday. They know from complete studics that the population standard deviation of this variable is 1.5 hours. previous and more (a) [Free Response.] In the context of this proł (b) Calculat lem, what dos μ represent? a 95% confidence interval, for the unknown population mean, μ, by answering the following three questions below. Round the upper and lower bound values to two decimal places. i. Find the appropriate tritical value using the t-table (table D). (Give your answer to 2 decimal places.) ii what is the value of the lower bound of the 95% confidence interval? Round your answer to 2 decimal places). iii, what is the value of the upper bound of the 95% confidence interval? (Round your answer to 2 decimal places).

Answer 1

a)

mu = 1.96 hours spent per weekday

b)
Critical value = 3.28

Lower BOund = mean - t *(s/sqrt(n))
= 1.96- 2.92 *(1.5/sqrt(256))
= 0.56

Upper Bound = mean + t *(s/sqrt(n))
= 1.96 + 2.92 *(1.5/sqrt(256))
=2.85

d)
1)
z score = 1.46

2)

Lower BOund = mean - t *(s/sqrt(n))
= 1.96 - 1.46 *(1.5/sqrt(256))
= 0.29

Upper Bound = mean + t *(s/sqrt(n))
= 1.96+ 1.46 *(1.5/sqrt(256))
=2.0007