Name_____________________________ One Sample Inference Project Due: March 25, 2014 20 points1. The average 1-year of is 29 inches tall. Assume that the height of all 1-year olds is randomly distributed. Use the random sample of the heights of 1 year olds listed below and at the 0.05 level of significance test the stated 29 inches?32 28 25.5 29.5 32 30 28.5a. State the null and alternate hypothesis.b. Find the test statistic.c. Find the critical value.d. Reject or fail to reject the null hypothesis and justify your answer based on the critical value.e. Record a conclusion without using the word hypothesis or claim.2. An experiment is conducted to study the effect of exercise on the reduction of cholesterol level in slightly obese patients considered to be at risk for heart attack. Eighty patients are put on a specified exercise regimen while maintaining a normal diet. At the end of 4 weeks the change in cholesterol level was recorded. The program goal is to reduce the cholesterol by more than 25 points. At the end of the program the average reduction was actually 27. The standard deviation for the population is 18. Use the .05 level of significance to conduct a test.a. State the null and alternate hypothesis.b. Find the test statistic.c. Find the p value.d. Reject or fail to reject the hypothesis and justify your answer using the p- value.e. Record a conclusion without using the word “hypothesis” or “claim”.3. The commute time recorded in minutes for several of Sam’s friends is listed below. Assume that the commute time is normally distributed and use this data to determine a 90% confidence interval estimate for the average commute time of Sam’s friends.32.6 22.1 67.4 34.2 21.1 11.24. Use the data in problem # 3. Find a 90% confidence interval estimate for the population standard deviation of the commute time using the data for Sam’s friends.5. Last’s week 125 out of 350 seats were occupied for a performance. Find a 90% confidence interval estimate for the population proportion of the seats that areoccupied for performances like this one6. The Energy Information Administration reported that 54.7% of homes in the U.S. were heated by natural gas. A random sample of 200 homes found that 115 were heated by natural gas. Use the data to test the Energy Information Administration’s percent at the .025 level of significance.a. State the null and alternate hypothesis.b. Find the test statistic.c. Find the p value or critical value.d. Reject or fail to reject the hypothesis and justify your answer based on the p-value or critical value.e. Record a conclusion without using the word hypothesis or claim.7. A recent study in a small city stated that the average age of robbery victims was 63.5 years. A sample of 21 recent victims has a mean of 63.7 years and a standard deviation of 1.9 years. At the .05 level of significance, is the average age higher than originally believed? Use the 5 steps and complete a hypothesis test using the p-value method or critical value method.8. A researcher wants to estimate the average weight loss obtained by patients at a residential weight loss clinic during the first week of a controlled diet and exercise regimen. How large a sample is needed to estimate this mean within 0.5 pounds with 95%confidence? Assume that these data are available from a preliminary observation of five individuals3.2 2.7 4.0 5.0 1.29. The Environmental Protection Agency recently identified 30,000 waste dumping sites in the United States that were considered to be at least potentially dangerous. How large asample is needed to estimate the percentage of these sites that do pose a serious threat to health within 2 percentage points with 90% confidence?10. The newest development in the treatment of acne is a drug called cis13-retinoic acid. A recent test of this drug with 14 patients suffering from severe acne showed 13 having dramatic clearing of active lesions. How many patients would need to be in a study to find a 90% confidence estimate of the population proportion of patients experiencing dramatic clearing if the estimate must be correct to within 2% or