According to the Centers for Disease Control and Prevention, 30% of Americans are habitually getting less than six hours of sleep a night – far less than the recommended seven to nine hours. New York is known as the city that never sleeps". In a random sample of 300 New Yorkers it was found that 105 of them get less than six hours of sleep a night. Is there significant evidence to suggest that the rate of sleep deprivation for New Yorkers is higher than the rate of sleep deprivation in the population at large?

(a) Write the hypotheses in symbols and in words.

(b) Are these assumptions and conditions for inference satisfied?

1) The population is at least 10 times of the sample.................Yes ............No

2) The sample is a simple random sample .................................Yes............No

3) np0> 10, n(1-p0) > 10.................................................................Yes............No

(c) Calculate the test statistic.

(d) Find and interpret the p-value in context.

(e) What is the 95% confidence interval of the percent of New Yorkers having sleep deprivation Should we use large sample or plus-four interval?

Answer rating: 100% (QA)

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