Question 5 Background: Late-Night Basketball Tweets Sleep deprivation affects ma
ID: 3357069 • Letter: Q
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Question 5 Background: Late-Night Basketball Tweets Sleep deprivation affects many different facets in life. Does it also affect professional athletes in their sport? Researchers at Stony Brook University wanted to study the effect of sleep of a player on the number of points scored in an NBA game. To gather information, a random sample of 112 NBA players with Twitter accounts was obtained. The researchers decided to use late-night tweets (between 11 pm and 7 am) as an indicator of less sleep the night before a game. For each player, their points scored was recorded for a game with at least one late-night tweets the evening before, and compared to their points scored in a game with no late-night tweet the evening before. The 90% confidence interval for the population average difference in points scored in a game ud (where the difference is defined as points scored in a game with late- night tweets the evening before minus points scored in a game with no late-night tweets the evening before) for the population of all NBA players was found to be (-1.3314,-0.6686) points.Explanation / Answer
a) Here we are given that confidence interval as: (-1.3314, -0.6686 )
Therefore, the margin of error here is computed as half of the confidence interrval width
MOE = ( -0.6686 + 1.3314)/ 2 = 0.3314
Therefore 0.3314 is the margin of error here.
b) The given statement is correct here, that we estimate with 90% confidence that the number of points scored in a game with late - night tweets the evening before could be 0.6686 to 1.3314 points lower than the number of points scored in a game with no late-night tweets the evening before. on average for the population of all NBA players. This is correct here as we computed the confidence interval to have negative figures.
c) The confidence interval is computed for population mean. Therefore this is correct.
d) The confidence interval is computed for population mean and not sample mean. Therefore this is not correct.
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