Sleep habits of New Yorkers

Sleep habits of New Yorkers#

New York is known as “the city that never sleeps”. A random sample of \({{ params.description.n }}\) New Yorkers were asked how much sleep they get per night. Statistical summaries of these data are shown below. The point estimate suggests New Yorkers sleep less than the recommended \({{ params.sleep_hours }}\) hours a night on average. Is the result statistically significant? Use \(\alpha={{ params.description.alpha }}\).

Part 1#

Write the hypotheses in symbols.

Answer Section#

  • \(H_0: \mu = 8\), \(H_a: \mu < 8\)

  • \(H_0: \mu < 8\), \(H_a: \mu > 8\)

  • \(H_0: \mu > 8\), \(H_a: \mu < 8\)

  • \(H_0: \mu = 8\), \(H_a: \mu = 8\)

Part 2#

Which of the following assumptions are required to conduct the appropriate hypothesis test?

Answer Section#

  • The data should be approximately normally distributed

  • The data should be obtained through random sampling methods

  • Observations within the sample should be independent of each other

  • The success-failure condition needs to be met

  • The population standard deviation must be known

Part 3#

Calculate the test statistic, \(T\).

Answer Section#

Part 4#

Calculate the degrees of freedom, \(df\).

Answer Section#

Part 5#

Find the p-value.

Answer Section#

Part 6#

Interpret the p-value in this context. Drawing a picture may be helpful.

Answer Section#

Part 7#

What is the conclusion of the hypothesis test?

Answer Section#

  • The probability that New Yorkers sleep exactly 8 hours per night.

  • The probability that the sample accurately represents the entire population of New Yorkers.

  • The probability of observing the obtained sample mean 7.92 hours if New Yorkers, on average, sleep 8 per night.

  • The probability of observing the obtained sample mean of 7.92 hours or more extreme, if New Yorkers, on average, sleep 7.92 hours per night.

Attribution#

Problem is from the OpenIntro Statistics textbook, licensed under the CC-BY 4.0 license.
Image representing the Creative Commons 4.0 BY license.