1. A researcher is interested in whether college students getenough sleep. She suspects that they get less than 8 hours of sleepon average. The sample mean (x¯) for 65 students was 7.08 hours.The standard deviation of number of hours students slept iss=1.8.
(a) Determine the null and alternative hypothesis for the test.What is the parameter in this study?
(b) The p-value for the test is <0.0001. Using a significancelevel of .05, write a one or two sentence conclusion in context ofthe problem.
(c) Calculate 95% confidence interval for µ, the mean number ofhours college students sleep per night. Interpret the confidenceinterval. Be sure to use the word mean or average in yourinterpretation and don’t forget units. If you are doing thecalculations by hand use t∗ = 1.998.
(d) Does your confidence interval support the results of thehypothesis test? Explain.
