Hours C entury S eniors Sleep

1. Rene Robledo Joana Ornelas Abraham Hernandez Per. 6 2011-2012 Hours Century Seniors Sleep

2. California Standards • 8.0 Students organize and describe distributions of data by using a number of different methods, Including frequency tables, histograms, standard line and bar graphs, stem-and-leaf displays, scatter plots, and box-and whisker plots. • 17.0 Students determine confidence intervals for a simple random sample from a normal distribution of data and determine the sample size required for a desired margin of error. • 18.0 Students determine the p-value for a statistics for a simple random sample from a normal distribution.

3. Data Collection • We collected data using the cluster and systematic sampling by asking every 3rd senior at century high school how many hours do they sleep per night.

4. Data • Hours that seniors sleep at night: • 4, 6, 7, 7, 8, 7, 9, 7, 9, 6, 10, 6, 8, 8, 4, 7, 6, 6, 5, 5, 6, 7, 8, 8, 6, 6, 5, 4, 7, 8, 8, 4, 5, 9, 6, 6, 6, 7, 5, 4

5. Histogram

6. Statistics • From our survey, students sleep for about 6.5 hours per night with a sample standard deviation of 1.5525 hours

7. Confidence Interval • 95% confidence interval • Z-Interval • (6.0189, 6.9811) • We are 95% confident that the population mean for the number of hours seniors sleep is between (6.0 ~ 7.0) hours

8. Hypothesis Testing • Hypothesis Testing: Test at α = .05 • 1) Hypothesis • Claim: We believe that the number of hours seniors sleep is 6 • Ho = µ = 6 • Ha = µ ≠ 6 • Test statistics (z-test) • P-value = .0417 > α = .05 • At 5% level of significance we fail to reject the Ho. There is enough evidence to support our claim.

9. Error Analysis • Our sample mean is 6.5 hours, and the 95% confidence level for the population mean is between 6.0189 to 6.9811 hours. The marginal error is about 0.4811 minutes. • Our sample error is due to possible underrepresentation of the population. We might need to take more samples because most seniors were from e-Business.

10. Conclusion • We hypothesized that Century seniors sleep an average of 6 hours. In our survey of 40 seniors, we found the sample mean of 6.5 hours with a standard deviation of 1.5525 hours. We concluded that the population mean for the number of hours seniors sleep is between 6-7 hours with 95% confidence. We test our initial hypothesis with 5% level significance, and confirm our hypothesis correct.