In this assignment students will demonstrate their understandingof the distribution of means doing all steps of hypothesistesting.
For each problem students will write out all steps of hypothesistesting including populations, hypotheses, cutoff scores, and allrelevant calculations. Assignments will be typed and uploaded in aword document to blackboard.

1.A nationwide survey in 1995 revealed thatU.S. grade-school children spend an average of µ = 8.4 hours perweek doing homework. The distribution is normal with σ = 3.2. Lastyear, a sample of n = 100 grade-school children was giventhe same survey. For this sample, the mean number of homework hourswas 7.1. Has there been a significant change in the homework habitsof grade-school children? Test with α = .05.

2.On the basis of her newly developedtechnique, a student believes she can reduce the amount of timeschizophrenics spend in an institution. As director of training ata nearby institution, you agree to let her try her method on 20schizophrenics, randomly sampled from your institution. The meanduration that schizophrenics stay at your institution is 85 weeks,with a standard deviation of 15 weeks. The scores are normallydistributed. The results of the experiment show that patientstreated by the student stay at the institution a mean duration of78 weeks. What do you conclude about the student’s technique? Use α= .05.

3.A psychologist has developed a standardizedtest for measuring the vocabulary skills of 4-year-old children.The scores on the test form a normal distribution with μ = 60 and σ= 10. A researcher would like to use this test to investigate theidea that children who grow up with no siblings develop vocabularyskills at a different rate than children in large families. Asample of n = 25 children is obtained, and the mean test score forthis sample is 63. On the basis of this sample, can the researcherconclude that vocabulary skills for children with no siblings aresignificantly different from those of the general population? Testat the .01 level of significance.

4.The average age for licensed drivers in acounty is 42.6, with a standard deviation of 12, and thedistribution is approximately normal. A county police officer wasinterested in whether the average age of those receiving speedingtickets is less that the average age of the population who has alicense. She obtained a sample of 16 drivers with speeding tickets.The average age for this sample was 34.4. Do all the steps ofhypothesis testing using the 0.01 significance level.