Adults tend to believe that a majority of teenagers sleep in on Saturdays, but maybe that is a misconception. A random sample of 120 teenagers showed that 48 slept in the previous Saturday. Use the computer output provided below to determine if there is convincing evidence at the α = 0.05 level that the true proportion of teenagers who slept in on the previous Saturday is less than 0.5.Use this computer output to answer the questions.Based upon the 95% confidence interval, it is reasonable to claim that the true proportion of all teenagers who slept in on the previous Saturday is between which two values?
The sample proportion is 48/120 = 0.40. A 95% confidence interval for the true proportion is approximately 0.40 ± 1.96√(0.40 × 0.60/120), which gives endpoints of about 0.3124 and 0.4877. Therefore, the correct choice is 0.3124 and 0.4877.
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