. Does playing Mozart for unborn babies result in children with higher IQs? A psychologist obtains a random sample of 20 mothers in the rst trimester of their pregnancy. The mothers are asked to play Mozart in the house at least 30 minutes each day until they give birth. After 5 years, the child is administered an IQ test. We know that IQs are normally distributed with a mean of 100. If the IQs of the 20 children in the study result in a sample mean of 104.2, and a sample standard deviation of 14.7, is there evidence that the children have higher IQs? Use a = 0.05 level of signicance. (2 pts) Write the claim statement in sentence. . (2 pts) State null and alternate hypothesis. (2 pts) Verify the requirements. . (2 pts) Find P-value. Explain why you should reject or not reject null hypothesis. (2 pts) Write the conclusion in sentence. . A simple random sample of size n = 12 is drawn form a population that is normally distributed. The sample variance is found to be 23.7. (4 pts) Construct a 90% condence interval for the population variance. Round to the two decimal places. . (2 pts) Interpret the condence interval. . (4 pts) A poll conducted in 2010, 64% of people polled answered yes to the following question: \"Are you in favor of the death penalty for a person convicted of murder?\" The margin of error in the poll was 3%, and the estimate was made with 95% condence. At least how many people were surveyed? . The quality-control manger determines that the piston diameters are normally distributed, with a mean of 0.5 inch and a standard deviation of 0.004 inch. The machine that controls the piston dirneter is recalibrated in an attempt to lower the standard deviation. Alter recalibration, the quality-control manager randomly selects 25 pistons form the production line and determines that the standard deviation is 0.0025 inch. Was the recalibration effective? Use the a = 0.01 level of signicance. (Hint: if the recalibration is effective, then it means standard deviation is lower.) (2 pts) Write the claim statement in sentence. . (2 pts) State null and alternate hypothesis. (2 pts) Verify the requirements