Question

The Doane Owl has hired you to conduct a study on Doane students’ use of technology as a result of classes moving online. You survey a randomly-selected probability sample of 150 Doane students. One question you ask is, “How many hours per day do you spend looking at a screen (phone, computer, tablet, TV, etc)?”. You find that your sample averages 7.63 hours of screen time per day (sd=3.27 hours).

a. Calculate and interpret the 90% confidence interval for screen time.

b. Calculate and interpret the 99% confidence interval for screen time.

c. As the confidence in your results increases, how does the size of the confidence interval change? Explain why this is so.

The Owl reporter asks you to write a short paragraph explaining the data and results to their readers who do not have a background in statistics. What would you write? (remember that a full interpretation should 1) set the scene, 2) present appropriate statistics in context, and 3) conclude in “plain language”)

Answer 1

Mean = 7.63

Sample size (n) = 150

Standard deviation (s) = 3.27

a)

Confidence interval(in %) = 90

z @ 90.0% = 1.645

Since we know that

  

Required confidence interval   

Required confidence interval = (7.63-0.4392, 7.63+0.4392)

Required confidence interval = (7.1908, 8.0692)

b)

Confidence interval(in %) = 99

z @ 99.0% = 2.576

Since we know that

Required confidence interval   

Required confidence interval = (7.63-0.6878, 7.63+0.6878)

Required confidence interval = (6.9422, 8.3178)

c)

As the confidence increases from 90% to 99% the size of interval also increases

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