Question

An article in the National Geographic News (February 24, 2005) reports that Americans are increasingly skimping on their sleep. A researcher wants to determine if Americans are sleeping less than the recommended 7 hours of sleep on weekdays. He takes a random sample of 150 Americans and computes the average sleep time of 6.7 hours on weekdays. Assume that the population is normally distributed with a known standard deviation of 2.1 hours. Use Table 1.

Answer 1

The test statistic is

  

P-value = P(Z < -1.75)

= 0.0401

At , since the p-value is less than , so we should reject the null hypothesis.

At 0.05 significance level, there is sufficient evidence to conclude that American are sleeping less than the recommended 7 hours of sleep on weekdays