Question

Social Media Addiction. Researchers are concerned about the impact of Social Media (Facebook, 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 problem has gotten worse with the recent widespread use of smartphones. The first objective of the 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 previous and more complete studies that the population standard deviation of this variable is 1.5 hours.

(b) Calculate 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 critical 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).

(d) One of the researchers is interested in an 85% confidence interval for the unknown population mean, µ.

i. Find the positive z-score (z ∗ ) for the corresponding confidence level. (Round your answer to 2 decimal places).

ii. Find the lower and the upper bound of the confidence interval. (Round your answer to 2 decimal places).

iii. [Free Response.] Suppose that the number of hours spent on social media on mobile on weekdays by all US college students does not follow a Normal distribution. Is the confidence interval trustworthy? That is, do you think you can really be 85% confident? Explain. (State Yes or No first followed by your explanation).

Answer 1

(b) Calculate 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 critical value using the t-table (table D). (Give your answer to 2 decimal places.) 1.9693106

ii. What is the value of the lower bound of the 95% confidence interval? (Round your answer to 2 decimal places) 2.9154

iii. What is the value of the upper bound of the 95% confidence interval? (Round your answer to 2 decimal places) 3.2846

(d) One of the researchers is interested in an 85% confidence interval for the unknown population mean, µ.

i. Find the positive z-score (z ∗ ) for the corresponding confidence level. (Round your answer to 2 decimal places) 1.4395315

ii. Find the lower and the upper bound of the confidence interval. (Round your answer to 2 decimal places) (2.965, 3.235)

iii. [Free Response.] Suppose that the number of hours spent on social media on mobile on weekdays by all US college students does not follow a Normal distribution. Is the confidence interval trustworthy? That is, do you think you can really be 85% confident? Explain. (State Yes or No first followed by your explanation).

No, if the distribution is not normal then the confidence interval is not valid. The underlying assumptions from building the confidence interval is the central limit therom that is based on the normal distribution. If this assumption is violated the confidence interval would not provide accurate results.