1.) The gas mileage for a certain model of car is known to have a standard deviation of 4 mi/gallon. A simple random sample of 81 cars of this model is chosen and found to have a mean gas mileage of 26.5 mi/gallon. Construct a 98% confidence interval for the mean gas mileage for this car model. 

2.) A 99% confidence interval for the mean of a population is to be constructed and must be accurate to within 0.3 unit. A preliminary sample standard deviation is 1.3. The smallest sample size n that provides the desired accuracy is ?

3.) An SRS of 30 students at UH gave an average height of 5.4 feet and a standard deviation of .3 feet. Construct a 90% confidence interval for the mean height of students at UH. 

4.) It is believed that the average amount of money spent per U.S. household per week on food is about $99, with standard deviation $10. A random sample of 25 households in a certain affluent community yields a mean weekly food budget of $100. We want to test the hypothesis that the mean weekly food budget for all households in this community is higher than the national average. State the null and alternative hypotheses for this test, the test statistic and determine if the results significant at the 5% level.

5.) Based on information from a large insurance company, 67% of all damage liability claims are made by single people under the age of 25. A random sample of 54 claims showed that 44 were made by single people under the age of 25. Does this indicate that the insurance claims of single people under the age of 25 is higher than the national percent reported by the large insurance company? State the null and alternate hypothesis then give the test statistic and your conclusion.