In 2016, the New York Times reported that the average American spent 50 minutes per day on Facebook, as compared to an average of 42 minutes per day reading, exercising, or actually socializing combined. You suspect that this gap has widened over the years, and collect a random sample of 100 people. For 50 of them (again, randomly chosen from your sample), you track their time spent on Facebook; you track the other 50 peoples’ total time spent reading/exercising/socializing. (a) Say the 2016 figures regarding Americans’ time allotments still hold true. If the population standard deviation for minutes using Facebook is 12.5 minutes, and the population standard deviation for minutes spent on reading, exercising, and socializing (referred to from here on as ”Other” activities) is 8 minutes, what are the expected value and the standard error of the difference between the average amount of time spent on Facebook and the average amount of time spent on Other activities computed from a sample like yours? (b) If the figures reported by the NY Times still hold true today, and assuming the standard deviations above, what is the probability that your random samples of time spent on Facebook and on Other activities will display an average difference larger than 12 minutes? (c) More efficient study designs are designs with smaller confidence interval widths. Say that you decide to use a paired differences design instead of with your 100 samples, i.e. you ask all participants about both their time on Facebook and on Other activities, and compute the difference for each person. Since the time spent on one activity leaves less time for other activities, we would assume that time spent on Facebook would be negatively correlated with time spent on Other activities. The worst-case scenario (in terms of efficiency) for paired-differences designs is when the two measurements have a perfect negative correlation; here, this would correspond to a population standard deviation of the differences equal to 20.5 (using the 2016 numbers). What is the sampling distribution of the mean of the paired differences, assuming perfect negative correlation in your sample of 100? Does this indicate that the paired-differences design will be more or less efficient?
In 2016, the New York Times reported that the average American spent 50 minutes per day on Facebook, as compared to an average of 42 minutes per day reading, exercising, or actually socializing combined. You suspect that this gap has widened over the years, and collect a random sample of 100 people. For 50 of them (again, randomly chosen from your sample), you track their time spent on Facebook; you track the other 50 peoples’ total time spent reading/exercising/socializing.
(a) Say the 2016 figures regarding Americans’ time allotments still hold true. If the population standard deviation for minutes using Facebook is 12.5 minutes, and the population standard deviation for minutes spent on reading, exercising, and socializing (referred to from here on as ”Other” activities) is 8 minutes, what are the
(b) If the figures reported by the NY Times still hold true today, and assuming the standard deviations above, what is the probability that your random samples of time spent on Facebook and on Other activities will display an average difference larger than 12 minutes?
(c) More efficient study designs are designs with smaller confidence interval widths. Say that you decide to use a paired differences design instead of with your 100 samples, i.e. you ask all participants about both their time on Facebook and on Other activities, and compute the difference for each person. Since the time spent on one activity leaves less time for other activities, we would assume that time spent on Facebook would be
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
